Undergraduate Program

Course Credit: 4

Course Description: This course deals with fundamental concepts and methods of statistics as a whole. The impact that statistics has made and will continue to make in Data Science and virtually in all elds of scienti c and human endeavors will be illustrated. A brief discussion on the introductory de nitions and meaning of terms and terminologies used in Applied Statistics and Data Science will be given. The basic topics in data, variables, their measurements, storage, management and methods for analyzing them will be presented. Course Objectives: The aim of the course is to provide a thorough theoretical grounding in data summarization and description for nding patterns in data. The primary objective is to provide an introduc- tion to summary measures necessary for the subsequent study of core and specialized courses in statistics and data science, namely, statistical machine learning, data science, probability, regression, generalized linear models, multvariate techniques, time series, econometrics and associated computing software. Contents: Introduction to data science: data science concept and its life cycle; big data and its sources; explain and demonstrate the value of data in assessing problems and supporting scienti c, commercial, social, and artistic problem-solving; distinguish between di erent types of data that are generated in science, engineering, and design; identify the types of questions that can be asked of data in satisfaction of a particular information goal; Employ strategies for ensuring data quality. Identify aspects of data governance to judge whether and how data can be used in analyses. Introduction to applied statistics: meaning of statistics; scopes and limitations; concepts of descriptive and inferential statistics; basic concepts: data, sources of data - primary and secondary data; population, sample, parameter, statistic; variables and types of variable: qualitative, quantitative discrete and continuous; scales of measurements; classi cation of variables by scales of measurements. Producing data: approaches of producing data; the concept of experimental study and non- experimental study to produce data; introduction to sample survey and questionnaire; the concept of electronically recorded data and hospital recorded data; the concept of data clean- ing and checking before statistical analysis. Organization and presentation of data: graphical presentation for qualitative and quantitative data; sorting data, grouping qualitative and quantitative data: construction of frequency dis- tribution and relative frequency distribution; graphical presentation of frequency distribution histogram, frequency polygon, ogive. Concept of distribution: location, scale (spread) and shape, illustration with stem-and-leaf diagram; descriptive measures of data; measures of location; measures of dispersion; mo- ments and their interrelationship; measures of skewness and kurtosis; three- and ve-number summary; box-plot and modi ed box-plot. Description of bivariate data: bivariate frequency distribution; graphical presentation of bi- variate data; contingency table; the concept of association between two variables; percentage table and interpretation of cell frequencies; measures of association for nominal and ordinal variables; measures of association for interval or ratio variables; correlation; the relationship between two variables: simple linear regression; basic issues in inferential statistics. Data visualization and analysis using spreadsheet (e.g., excel, google sheets, etc.)

Course Credit: 4

Course Description: This is an introductory course on probability theory. This course attempts to provide basic concepts of set theory, experiment and sample space, and di erent approaches of de ning probability. It discusses useful laws of probability, conditional probability, Bayes rule, random variables and their distributions, and functions of random valuables. It also covers discussions on certain operators like mathematical expectation and generating function with properties and applications, and thorough discussions on commonly used probability distributions such as binomial, hypergeometric, and negative binomial, Poisson, normal, exponential and gamma distributions. Course Objectives: To provide basic concepts of sets, counting techniques, and acquaint students with necessary skills for solving probability related problems using appropriate laws. To introduce the notions of random variables. To develop ability to nd probability distribution of random variables and of their functions. To introduce operators like generating functions, expectation, etc. for studying the characteristics of distributions. To make familiar with basic probability distributions with possible areas of applications. To prepare the students for learning advance courses where probability theory has a prominent role. Course Learning Outcomes (CLOs) Students who successfully complete this course should be able to CLO1 understand (explain ideas and concept) Students will be able to explain basic con- cepts of set theory, experiment and sample space, di erent approaches of de ning probability, and useful laws of probability. CLO2 analyze (draw connection among ideas) Students will be able to analyze and draw connections between concepts such as conditional probability, Bayes rule, random variables, and their distributions. CLO3 evaluate (justify a stand or decision) Students will be able to justify their decisions by evaluating the probability distributions of random variables and the use of operators like mathematical expectation and generating functions. CLO4 apply (use information in new situation) Students will be able to apply the concepts and laws of probability to solve problems and nd probability distributions of random variables in new situations. CLO5 create (produce a new or original work) Students will be able to create new insights and original work by using generating functions and studying characteristics of various probability distributions. Contents: Combinatorial analysis: basic principles of counting, permutations, combinations; axioms of probability: sample space and events, axioms of probability, sample spaces having equally likely outcomes, probability as a measure of belief; conditional probability and independence: conditional probabilities, Bayes formula, independent events. Random variables: introduction, discrete random variables, expectation, expectation of a function of a random variable, variance, Bernoulli and binomial random variables, Poisson random variable, other discrete random variables (geometric, negative binomial, hypergeo- metric); expected value of a sums of random variables; properties of cumulative distributionfunction; continuous random variables: expectation and variance of continuous random vari- able, normal random variable, normal approximation to binomial distribution, exponential random variables. Jointly distributed random variables: joint distribution functions, independent random vari- ables, sums of independent random variables, conditional distributions (discrete and contin- uous cases); properties of expectation: expectation of sums of random variables, covariance, variance of sums, correlations, conditional expectation, moment generating functions, proba- bility generating function.

Course Credit: 3

Course Description: The Foundation of Mathematics course is meticulously designed to provide a thorough ex- ploration of three fundamental pillars in mathematics: algebra, di erential equations, and discrete mathematics. This course covers the theory of numbers, theory of equations, se- ries, formulation of simple applied problems in terms of di erential equations and solving approaches, discrete mathematical structures, such as sets, graphs, and combinatorics to pre- pare students for developing problem-solving skills by applying mathematical concepts to real-world problems, and enhancing analytical thinking and logical reasoning skills. Course Objectives: The objective of the course is to equip students with a solid understanding of the fundamental concepts, theories, and applications of these mathematical areas so that students can develop a strong foundation for advanced topics in statistics and computing. Learning Outcomes After completion of the course, students are expected to CLO1 learn and understand the theory of numbers, di erential equations and discrete mathematics in detail CLO2 understand and apply di erent mathematical structures, such as sets, graphs, and combinatorics, to solve problems in computer science, cryptography, and other related elds CLO3 develop problem-solving skills by applying mathematical concepts to real-world problems CLO4 to enhance analytical thinking and logical reasoning skills. Contents Part A (Basic Algebra) Theory of numbers: unique factorization theorem; congruences; Euler's phi-function; inequal- ities: order properties of real numbers; Weierstrass', Chebysev's and Cauchy's inequalities; inequalities involving means; complex numbers: eld properties; geometric representation of complex numbers; operations of complex numbers; summation of algebraic and trigonometric nite series; theory of equations: relations between roots and coe cients; symmetric functions of roots; Descartes rule of signs; rational roots; Beta and gamma function and their properties; incomplete beta and gamma function ; Dirich- let's theorem. Part B (Di erential Equations) Formulation of simple applied problems in terms of di erential equations; equations of the rst order and their solutions; singular solutions; geometric applications; linear equations with constant coe cients; method of undetermined coe cients; variation of parameters, simple cases of linear equations with variable coe cients.Part C (Discrete Mathematics) Combinatorics: Counting principles. Inclusion-exclusion principle. Pigeonhole principle. Generating functions. Recurrence relations. Graphs, structure, and symmetry of graphs, trees and connectivity, Eulerian and Hamiltonian graphs and diagraphs, directed graphs, and planar graphs. Algorithms on graphs: Introduction to graphs, paths and trees. Shortest path problems: Di- jkstra'a algorithm, Floyd-Warshall algorithm and their comparisons. Spanning tree problems. Kruskal's greedy algorithm, Prim's greedy algorithm and their comparison. *In addition to the compulsory question, students should answer at least one question from each of the part.

Course Credit: 3

Introduction: The course is designed to provide a comprehensive foundation in the concepts and techniques of calculus. Key topics include basic functions, their graphs, and properties, as well as curve sketching, limits, continuity, di erentiation, and relative extrema. Applications of di erenti- ation and the Taylor Series are also covered. Additionally, the course expands calculus from the two-dimensional world of single-variable functions into the three-dimensional world and beyond, addressing multivariable functions.This course aims to equip students with a robust understanding of both single-variable and multivariable calculus, preparing them for advanced mathematical and analytical challenges. Objectives: This course aims to develop both computational pro ciency and a deep geometric understand- ing of calculus, equipping students with essential mathematical skills for advanced studies in statistics. Emphasizing the ability to perform complex calculations accurately and visualize geometric interpretations of functions and surfaces. Students will learn to apply these tech- niques to real-world problems and statistical analyses, including curve tting and di erential equations. Learning Outcomes: Upon completion of the course, students will be able to CLO1 execute di erentiation for single-variable and multivariable functions, and apply these techniques to solve real-world problems CLO2 understand and analyze the geometric interpretations of calculus, including the be- havior of functions, shapes of curves, and properties of surfaces in three-dimensional space. CLO3 employ optimization techniques, including the use of Lagrange multipliers, to solve complex problems involving maxima and minima in various contexts. CLO4 cultivate a logical and systematic approach to problem-solving, enhancing their ability to tackle advanced mathematical challenges in academic and professional settings. Contents Functions and their graphs: polynomial and rational functions, logarithmic and exponential functions, trigonometric functions and their inverses, hyperbolic functions and their inverses, composition of functions. Limit and Continuity of Functions: De nition. Basic limit theorems, limit at in nity and in- nite limits. Continuous functions. Properties of continuous functions on closed and bounded intervals. Di erentiability and related theorems: Tangent lines and rates of change. De nition of deriva- tive. One-sided derivatives. Rules of di erentiation. Successive di erentiation. Leibnitz the- orem. Related rates. Linear approximations and di erentials. Rolle's theorem, Lagrange's and Cauchy's mean value theorems. Extrema of functions, problems involving maxima and minima. Concavity and points of in ection. Indeterminate forms. L'Hospital's rule. Power series expansion: Taylor's theorem with general form of the remainder; Lagrange's and Cauchy's forms of the remainder. Taylor's series. Maclaurin series. 5. Applications: Physical, Biological, Social Sciences, Business and Industry. Vector-valued functions: Introduction to Vector-Valued Functions, Calculus of Vector-Valued Functions, Tangent lines to graphs of vector-valued functions. Arc length from vector view point. Arc length parameterization. Curvature: Unit Tangent, Normal and Binormal Vectors, Curvature of plane and space curves: Curvature from intrinsic, Cartesian, Parametric and Polar equations. Radius of curvature. Centre of curvature. Partial Di erentiation: Functions of several variables, Graphs of functions of two variables, Limits and continuity, Partial derivatives, Di erentiability, linearization and di erentials. The Chain rule. Partial derivatives with constrained variables, Directional Derivatives and Gradi- ents, Tangent Planes and Normal Vectors, Extrema of functions of several variables, Lagrange multipliers. Taylor's formula for functions of two variables.

Course Credit: 3

Course Description: This course introduces students to Integral Calculus, focusing on the techniques of integration and their applications to solving physical problems. Key topics include nding areas under curves, lengths of curves, volumes, and surface areas using integration methods. Students will gain a comprehensive understanding of integral calculus concepts and develop the skills needed to apply these techniques to various mathematical and real-world scenarios. Course Objectives: The course aims to equip students with a robust understanding of Integral Calculus and its applications. By the end of the course, students will be able to interpret de nite integrals geometrically as areas under curves and construct them as limits of Riemann sums. They will understand di erentiation and anti-di erentiation as inverse operations, as outlined in the Fundamental Theorem of Calculus, and will be pro cient in evaluating integrals using various techniques. Additionally, students will be able to recognize and solve di erent types of improper integrals, calculate areas between curves, volumes of solids of revolution, surface areas, and arc lengths using integration. They will also develop the ability to solve problems involving multiple integrations in rectangular, cylindrical, and spherical coordinate systems, and apply appropriate models. Learning Outcomes Upon completion of the course, students will be able to CLO1 interpret the de nite integral geometrically as the area under a curve and construct de nite integrals as the limit of Riemann sums. CLO2 select and apply appropriate models and techniques to de ne and evaluate line and surface integrals. CLO3 solve problems involving multiple integrations using rectangular, cylindrical, and spherical coordinate systems. CLO4 calculate areas between curves, volumes of solids of revolution, surface areas, and arc lengths using integration. Contents: The anti derivatives (inde nite integral): Techniques of integration; integration by parts; integration by substitution; integration of rational functions, Integration by reduction. De nite integration: using antiderivatives. De nite integration using Riemann sums. Funda- mental theorems of calculus. Basic properties of integration. Applications of integration: Plane areas. Solids of revolution. Volumes by cylindrical shells. Volumes by cross-sections. Arc length and surface of revolution. Improper integrals: Improper integrals of di erent kinds. Gamma and Beta functions. Integrals in polar coordinates: Area and arc length in polar coordinates. Double Integrals: Double Integrals over Nonrectangular Regions, Double Integrals in Polar Coordinates, Surface Area; Parametric Surfaces and Applications of Double Integrals. Triple integrals: Volume as a triple integral, Triple Integrals in Cylindrical and Spherical Coordinates, Centers of Gravity Using Multiple Integrals and Applications of Triple Integrals, Change of Variables in Multiple Integrals; Jacobians. Topics in vector calculus: Vector Fields, Gradient, Divergence, curl and their physical mean- ings Line Integrals, Green's Theorem.

Course Credit: 3

Course Description: Linear algebra can be used in pretty much any application that deals with more than one random variable at a time rather than dealing with a random vector. Particularly, linear algebra will be heavily used in multivariate statistics course(s). Some matrix algebra will also be very convenient for potential studies in Markov chains and stochastic processes. Linear regression is a very common use of linear algebra as well. Course Objectives: To solve systems of linear equations using various methods, including Gaussian and Gauss- Jordan elimination and inverse matrices. To perform matrix algebra, determinants, and their properties. To understand and apply properties of real vector spaces and subspaces, including linear independence and dependence. To nd eigenvalues and eigenvectors and use them in applications. Learning Outcomes: Upon completion of MATH 106, students will be able to CLO1 solve systems of linear equations using Gaussian and Gauss-Jordan elimination and inverse matrices CLO2 Perform matrix algebra, determinants, and understand their properties (Concept). CLO3 Understand and apply properties of real vector spaces and subspaces, including linear independence and dependence CLO4 Find eigenvalues and eigenvectors and apply them in various scenarios (Applica- tion). CLO5 Create orthogonal and orthonormal bases using the Gram-Schmidt process and solve application problems Contents Matrices, vectors and their operations: basic de nitions and di erent types of matrices, matrix operations (addition, multiplication), trace of a matrix, determinant and adjoint of a square matrix, properties of determinants, inverse of matrix, properties of inverse, Kronecker product and related operations. System of linear equations: Gaussian elimination, Gauss-Jordan elimination, homogeneous linear systems, null spaces and the general solution of linear systems, rank and linear systems, generalized inverse of a matrix, generalized inverses and linear systems. Vector spaces and subspaces: vector addition and scalar multiplication, linear spaces and subspaces, intersection and sum of subspaces, linear independence and dependence, basis and dimension, inner product, norms and orthogonality, orthogonal projections, Gram-Schmidt orthogonalization. Eigenvalues and eigenvectors: eigenvalue equation, characteristic polynomial and its roots, Eigenspaces and multiplicities, diagonalizable matrices, computation of eigenvalues and eigen- vectors. Singular value and Jordan decompositions: singular value decomposition, SVD and linear systems, computing the SVD, Jordan canonical form. Quadratic forms: matrices in quadratic forms, positive and nonnegative de nite matrices, congruence and Sylvester's law of inertia, nonnegative de nite matrices and minors, some in-equalities related to quadratic forms, simultaneous diagonalization and the generalized eigen- value problem.

Course Credit: 4

Course Description: This course provides an introduction to a broad range of economic concepts, description of economic laws and theories, and analytical reasoning behind those. It considers both microeconomics: the supply and demand-based choices made by individual units (households and rms), and macroeconomics: the broader analysis of the economy. The use of supply and demand models will be the fundamental tools and the trade-o s and choices will be considered through comparison of costs and bene ts measures. Production and market structure will be analyzed at the rm level as well. Macroeconomic issues concerning the interaction of goods and services markets, labor supply and economic resources at an aggregate level (region or country level) will be discussed. Course Objectives: The objectives of the course are to introduce students to principal microeconomic theories and demonstrate how these laws can be used to explain economic choices made by households and rms; to describe how macroeconomic concepts can be used to analyze economy as a whole; to help students learn how to interpret economic models, diagrams and tables and use them to analyze di erent economic phenomena; and to illustrate how government policies in uence microeconomic choices and macroeconomic upshots. Learning Outcomes: After completion of the course, students are expected to CLO1 understand theories and principles in microeconomics including consumer theory, production cost, price theory, market structure, trade-o s, comparative advantage, factor markets, public goods, externalities and market failure. CLO2 learn macroeconomic concepts and principles including productivity, in ation, em- ployment and government economic policies. CLO3 acquire quantitative skills used in economic modelling and analysis. CLO4 understand scal and monetary policies of Bangladesh and how they are related to relevant SDG goals. CLO5 demonstrate the skills to apply and explain macroeconomic and microeconomic principles to analyse di erent individual, rm or state-level economic issues.Contents De nition and scope of economics; theory of demand and supply; demand schedule; supply schedule; equilibrium of demand and supply; elasticity of demand and supply: measurement of elasticity; price elasticity of demand and supply. Demand and consumer behavior; utility theory; equi-marginal principle; indi erence curve analysis: consumers surplus; individual and market demand; derivation of demand curve; theory of production: production function; total, average and marginal product; law of di- minishing returns; factors of production; pricing of factors of production; division of labor; localization of industries; returns to scale; law of variable proportion; isoquants; Cob-Douglas and CES production function; theory of cost; xed and variable cost; total and marginal costs; least cost rule; opportunity cost. Market structure: perfect and imperfect competition; pricing under monopoly, oligopoly and monopolistic competition; short-run and long-run equilibrium analysis; income and wealth: factor incomes vs. personal incomes, role of government, wealth; fundamentals of wage deter- mination, the supply of labor, determinants of supply, empirical ndings, wage di erentials; basic concepts of interest and capital, prices and rentals on investments, rates of return and interest rates, present value of assets, real vs. nominal interest rates. Key concepts of macroeconomics: objectives and instruments of macroeconomics; measuring economic success, tools of macroeconomic policy; real vs. nominal GDP, \De ating" GDP by a price index; consumption, investment, NDP, GNP, price indexes and in ation; consumption and saving: consumption function, saving function; investment: determinants of investment, revenues; theories of economic growth: four wheels of growth, human and natural resources, capital; theories of economic growth: classical dynamics of Smith and Malthus, neoclassical growth model. Index number: characteristics and uses, problems in the construction, classi cation; methods: unweighted, weighted: Laspeyre's, Paasche's, Dorbish and Bowley's, Fisher's, Marshall and Edgeworth's, Kelly's and the chain index numbers; test of accuracy, base shifting, splicing, de ating of index numbers; application of consumer price index number.

Course Credit: 2

Course Description: Programming with C/C++ course mainly focuses on the programming language C. The course introduces machine level language, origin of C and applications of C programming in statistics. Course Objectives: This module covers introductory ideas to connect C programming with statistics through programming code execution. To understand how to analyze descriptive statistics and data analysis using C programming. Learning Outcomes: After completion of the course, students are expected to CLO1 be introduced with the C programming language. CLO2 know techniques that facilitate the development of structured computer programs, such as algorithms, pseudocode, owchart, etc. Understand how to control C programs, write C functions, use arrays. CLO3 how to connect C programming with statistics through programming code execu- tion. CLO4 unders tand how to analyze descriptive statistics and data analysis using C pro- gramming. Contents: Introduction to programming: algorithm, owchart, code (program); levels of programming: machine level, assembly level and high level language; execution of code: translator, compiler, interpreter, assembler; steps of execution: compilation, link, run. An overview of C: the origins of the C language, compilers versus interpreters; variables, constants, operators, and expressions: data types, declaration of variables, assignment state- ments, constants, operators, expressions; program control statements: C statements, con- ditional statements, loop statements, labels; functions: the return statement, function ar- guments, arguments to main(), returning pointers, pointers to functions; arrays: single- dimension arrays, passing single dimension arrays to functions, two- and multi-dimensional arrays, arrays and pointers, allocated arrays, array initialization.Applications of C programming in data analysis: frequency distributions, data summary, e.g. mean, median, maximum, minimum, matrix operations, calculation of di erent rates, tting simple linear regression and sorting a vector.

Course Credit: 2

Course Description: In today's data-driven world, business enterprises and industries can access more data than ever. However, they need skilled professionals who can manage and analyze data using various tools and techniques to make sense of all this data. Structured Query Language (SQL) is a widely used tool in data science for managing and querying data stored in relational databases. This course is designed to introduce students to SQL and its application in data science. Course Objectives: To teach students the basics of SQL through hands-on exercises and real-world examples. To cover advanced topics such as SQL joins, subqueries, and aggregation functions. To provide students with a comprehensive understanding of SQL and its pivotal role in data science. Learning Outcomes Upon completion of CSE-131, students will be able to CLO1 understand the basic concepts of SQL, such as tables, queries, and basic SQL syntax (Concept). CLO2 retrieve and manipulate data from databases using SQL queries, including ltering, sorting, and joining data from multiple tables (Application). CLO3 perform basic data analysis using SQL, including calculating summary statistics and aggregating data (Compute, Application). CLO4 understand how SQL ts into the data science work ow (Concept) Contents Introduction to database systems and relational databases; fundamentals of SQL and MySQL; MySQL data types; creation of database tables; populating, updating, and modifying tables; query mechanics and query execution. Use of SQL clauses including SELECT, FROM, WHERE, GROUP BY, ORDER BY, and HAVING; implementation of SQL joins; use of subqueries; application of aggregate functions including MIN, MAX, SUM, COUNT, AVG; handling date and time functions. Creation and use of views; transaction management; indexing and performance considerations. Application of SQL for data analysis, including computation of summary statistics, univariate and bivariate frequency distributions, correlation analysis, and basic regression analysis using database tables.

Course Credit: 2

Each student must be examined by a committee of selected members at the end of the aca- demic year.

Course Credit: 3

Course Description: This course provides a comprehensive introduction to sampling distributions-a fundamental concept in statistical theory that underpins the process of making inferences and drawing conclusions from sample data. Sampling distributions play a critical role in statistical analysis by providing a bridge between sample data and population parameters. Contents will involve deriving the theoretical properties of di erent distributions, examining the inter-relationship between them and focusing on their applications in statistical inference. Course Objectives: This course's main objective is to acquaint students with the main concepts and uses of probability and sampling distributions. More speci c objectives include demonstrating the derivation of sampling distributions of sample statistics, describing properties of common sampling distributions and illustrating the role and use of sampling distributions in inferential statistics. Learning Outcomesf: After completion of the course, the students are expected to CLO1 learn about di erent generating function techniques and their role in mathematical derivation of distributions of functions of random variables CLO2 understand the theoretical and practical concepts of probability and sampling dis- tributions CLO3 gain insights into the central limit theorem and its implications CLO4 learn about mathematical properties of common sampling distributions and inter- relationships CLO5 understand the application of sampling distribution in statistical inference Contents: Generating function techniques: moment generating function, cumulant generating function, probability generating function, characteristic function; nding distributions of functions of random variables: change of variable technique, distribution function technique, and moment- generating function technique; probability integral transformation; statistic and sampling distribution; law of large numbers; central limit theorem; exact distribution of sample mean; chi-square distribution and its properties; F-distribution and its properties; t-distribution and its properties; non-central chi-square, F and t distributions: de nition and derivation; concept of order statistics, distributions of single order statistics, and joint distribution of two or more order statistics. A brief review of some probability distributions and their properties: uniform, normal, expo- nential, gamma, beta, log-normal, Cauchy; de nition of truncated distribution; de nition of compound and mixture distribution; family of distributions: Pearsonian distribution.

Course Credit: 3

Course Description: This course aims at providing an introduction to principles of actuarial science and mathemat- ics involved in it. Topics include role of insurance in economy, di erent instruments involved in actuarial computations including interest and discount rates, pricing and valuation of actu- arial products including annuities, amortization schedules, sinking funds, life assurances and premiums, among others. Course Objectives: The course will enable understanding of the fundamental concepts of actuarial science and appreciate its role in economy. It will build a concrete knowledge of underlying theories behind actuarial computations. Finally, it will help to understand how statistical and mathematical models are used in pricing and valuing actuarial products and their real life applications. Learning Outcomes: Upon completion of this course the students should be able to CLO1 understand the fundamental concepts of actuarial science and appreciate its role in economy, CLO2 obtain concrete knowledge of underlying theories behind actuarial computations. CLO3 understand how statistical and mathematical models are used in pricing and valuing actuarial products and their applications in various real-life actuarial problems. Contents The meaning of actuarial science; role of insurance in the economy; role of an actuary. Fundamentals of theory of interest: de nition of simple interest and compound interest and their comparisons; accumulated value factors and present value factors; e ective and nominal rates of interest and their interrelationship; e ective and nominal rates of discount; relation between interest and discount; equations of value and use of the time diagram in solutions of problems in interest; problems involving unknown length of investment and unknown rate of interest; annuity; di erent types of annuities certain; present and accumulated values of immediate annuity and annuity due; present value of deferred annuities and variable annuities; capital redemption policies; amortization schedules and sinking funds. Actuarial mathematics: discrete life annuity and its applications; present values of di erent life annuities; life assurance; present values of various life assurances in terms of commutation functions; related problems; premiums; di erent types of premiums; net premiums; o ce premiums; prospective policy values. The basic deterministic model: cash ows; an analogy with currencies; discount functions; calculating the discount function; interest and discount rates; constant interest; values and actuarial equivalence; regular pattern cash ows; balances and reserves; basic concepts; rela- tionship between balances and reserves. Stochastic interest-rate models: stochastic interest-rate models I; basic model for one stochas- tic interest rate; independent interest rates; stochastic interest-rate models II; dependent annual interest rates; modelling the force of interest; what one can do with these models.

Course Credit: 4

Course Description: This course deals with fundamental concepts and techniques of statistical inference including estimation and tests of simple and composite hypotheses. A brief revision will also be given of some basic topics in probability theory as well as random variables. Course Objectives: The aim of the course is to provide a thorough theoretical grounding in statistical inference. The primary objective is to provide an introduction to mathematical statistics necessary for the subsequent study of specialized courses in statistics, bio-statistics, actuarial science and econometrics. The impact that statistics has made and will continue to make in virtually all elds of scienti c and other human endeavors is considered. Learning Outcomes: After completion of the course, students are expected to CLO1 know the most common parametric and nonparametric distributions CLO2 explore the concepts of the likelihood principle, the maximum likelihood, least square and the method of moments CLO3 develop the skill to handle a parametric hypothesis testing problem CLO4 illustrate inferential theory and implement the asymptotical concepts in practices CLO5 improve the computing ability using con dence interval and goodness of t notions Contents Basic Concepts: Fundamental ideas of statistical inference; parametric and non-parametric in- ference; estimators, statistics, parameters, theory and reality; sampling distributions and uses in inference; Estimation: Estimation of parameters and tting of probability distributions; parameter estimation: method of moments, method of least squares, method of maximum likelihood - properties of maximum likelihood estimators, Bayes estimator; properties of a good point estimator; method of evaluating estimators: mean squared error; best unbiased estimator - e ciency and the Cramer-Rao lower bound; su ciency - su cient statistics, prop- erties of su cient statistics, exponential family and factorization theorem, the Rao-Blackwell theorem, minimal su cient statistics, complete statistics. Interval estimation: introduction; method of constructing con dence interval - pivotal quan- tity, exact and approximate con dence interval; large- and small-sample con dence intervals; selecting the sample size; simultaneous con dence region. Test of Hypothesis: Elements of statistical hypothesis test; approaches to hypothesis testing: Neyman-Pearson approach, Fisher approach, and Je reys' approach; common tests based on normal distribution: one-sample settings, two-sample (independent and paired) settings, more than two sample settings; the duality of con dence intervals and hypothesis tests; exact and large sample test; evaluating statistical test procedure - the power of tests, optimal test - Neyman-Pearson lemma; most powerful tests; composite hypotheses; generalized likelihood ratio test; uniformly most powerful tests; unbiased tests; goodness-of- t tests - probability plots, test for normality, chi-square goodness of t test, Kolmogorov-Smirnov test; statistical tests applied to categorical data problems: introduction, Fisher's exact test, the chi-square test of homogeneity, chi-square test of independence.

Course Credit: 3

Description: The design of an experiment involves considering the set of treatments selected for compari- son, specifying the units to which the treatments are to be applied, determining the rules for allocating treatments to units, and specifying the measurements to be made on each unit. Var- ious designs are now standard in a wide range of practical situations in agriculture, medicine, engineering, and other elds. This course covers methodological and practical issues in the design and analysis of experiments. Topics covered include an introduction to the design of experiments, completely randomized design, randomized complete block design, Latin square design, and balanced incomplete block design. Course Objectives: The course aims to help students understand the methodological issues of experimental design. Students will develop the skills to write hypotheses that can be tested using experiments and to analyze and interpret data obtained from experiments. Learning Outcomes: After completing the course, students are expected to CLO1 identify the response variable, factor(s) of interest, and nuisance factors, and choose the most suitable experimental design for the given problem. CLO2 set up the relevant null and alternative hypotheses, obtain an ANOVA table, and construct appropriate (orthogonal) contrasts. CLO3 carry out multiple comparisons, check model assumptions graphically and formally, and apply a suitable transformation when needed. CLO4 determine the appropriate sample size, analyze data, and state conclusions in the language of the problem posed. CLO5 demonstrate skills in designing and implementing a standard experimental design and explaining it to di erent stakeholders in various sectors.Contents Introduction to design of experiments: strategy of experimentation; some typical examples of experimental design; basic principles; guidelines for designing experiments. Experiments with a single factor: the analysis of variance; analysis of xed e ects model; estimation of model parameters; unbalanced data; model adequacy checking; regression model, comparisons among treatment means, graphical comparisons of means, contrasts, orthogonal contrasts, multiple testing, Sche e's method, comparing pairs of treatment means, comparing treatment means with a control; Determining sample size; operating characteristic curve, specifying standard deviation increase, con dence interval estimation method; discovering dispersion e ects; regression approach to analysis of variance; least squares estimation of the model parameters, general regression signi cance test. Randomized blocks, Latin squares, and related designs: the randomized complete block de- signs (RCBD); statistical analysis of RCBD, model adequacy checking; estimating model pa- rameters; Latin square design; Graeco-Latin square design; balanced incomplete block design (BIBD); statistical analysis of BIBD; least squares estimation of BIBD; recovery of intra-block information in the BIBD.

Course Credit: 4

Course Description: Understanding a nation's population patterns, socioeconomic growth, and public health all depend heavily on its demographic data. To analyze this data, this course de nes demographic life events and describes statistical analysis methodologies. Course Objectives: The course is intended to introduce the basic ideas of demography and state the importance of demographic studies. It helps to understand well-known demographic theories and di erent measures of demographic events. Students will perceive and analyze current demographic situation of Bangladesh. Learning Outcomes: Upon successful completion of the course, the students are expected to CLO1 know demographic data sources and collection procedures CLO2 measure di erent fertility, mortality and nuptiality statistics CLO3 learn migration statistics and e ect on population growth migration statistics and e ect on population growth CLO4 compute and interpret di erent types of fertility data and use them in real life scenarios.Contents The basic concept of demography; role and importance of demographic/population studies; sources of demographic data: census, vital registration system, sample surveys, population registers, and other sources, especially in Bangladesh. Errors in demographic data: types of errors and methods of testing the accuracy of demo- graphic data; quality checking and adjustment of population data; post-enumeration check (PEC) and detection of errors and de ciencies in data and the needed adjustments and cor- rections. Fertility: basic measures of fertility, crude birth rate, age-speci c fertility rates (ASFR), the general fertility rate (GFR), the total fertility rate (TFR), the gross reproduction rate (GRR), and net reproduction rate (NRR), child-woman ratio; the concept of fecundity and its relationship with fertility. Fertility trends and patterns in Bangladesh. Demographic theory: transition theory and the present situation in Bangladesh; Malthus' theory and its criticism. Mortality: basic measures of mortality: crude death rate (CDR), age-speci c death rates (ASDR), infant mortality rate, child mortality rate, neonatal mor- tality rate; standardized death rate its need and use; direct and indirect standardization of rates; commonly used ratios: sex ratio, child-woman ratio, dependency ratio, and density of population. Mortality trends and patterns in Bangladesh. Nuptiality: marriage, types of marriage, age of marriage, age at marriage and its e ect on fertility, celibacy, widowhood, divorce, and separation, their e ect on fertility and population growth. Migration: de nition, internal and international migration; sources of migration data; factors a ecting both internal and international migration, laws of migration; the impact of migration on origin and destination, its e ect on population growth, age and sex structure, labor supply, employment and unemployment, wage levels, and other socio-economic e ects; migration of Bangladeshis abroad and its impact on the overall economic development of the country. Graduation of data: meaning and its need, techniques of graduation, graduation of age dis- tribution; life table: its concept, structure, and calculation; complete life table (life table by single year of age) and abridged life table, multiple decrement life tables, working life table, di erent life table functions and inter-relationships among them, use of life table, etc. Model life tables, Coale and Demeny regional model life tables. Stable and stationary populations.

Course Credit: 3

Course Description: Sampling refers to the statistical techniques used in survey research in many areas such as business, marketing, environmental science, political polls, and many areas of social science and public health. This course introduces di erent sampling techniques and approaches to designing a sample survey and methods for analyzing survey data from both a theoretical and applied perspective. This course covers topics related to general procedures in sample surveys, some basic sampling techniques, sample size determination, and methods of estimation of parameters of interest under each sampling scheme. Course Objectives: The objectives of the course are to make students familiar with di erent sampling techniques, sample size determination, and estimating the parameters of interest and their use in practice, and to prepare students to demonstrate their skills for designing all basic sample surveys, analyzing the data, and explain them to various stakeholders and other researchers in diverse areas. Learning Outcomes: After completion of the course, students are expected to CLO1 understand the concept of a sample survey and the general steps of conducting a survey CLO2 know in detail about di erent sampling techniques and their use in practice to design a survey CLO3 understand the methods of estimating the parameters of interest under di erent sampling schemes. CLO4 develop skills to determine the sample size, calculate sampling weight, and apply them in practice CLO5 demonstrate skills for designing and implementing a standard sample survey and explaining it to di erent stakeholders in many sectors. Contents: Introduction: concept of sampling, and de nition of related terms; role of sampling theory, requirements of a good sampling design, steps in a sample survey, probability and nonproba- bility sampling, selection (draw-to-draw) and inclusion probability, sampling weight, with and without replacement sampling, characteristics of estimate: bias, mean square error and variance (precision), errors in sample survey and census, sample size determination: basics and complex scenarios. Simple random sampling (SRS): sample selection, estimation: mean, total, proportion, ratio of two quantities, unbiasedness and variances/standard errors (SEs) of the estimators, esti- mators of the SEs, con dence interval (normal approximation); nite population correction, estimation over subpopulation, computation: inclusion probabilities and sampling weights. Systematic sampling: motivation, use and challenges, sample selection, di erent estimators and their unbiasedness and variances, estimator of the variances, comparison with SRS, sam- pling from population with linear trend or periodic variation. Strati ed random sampling: concept, reasoning and needs in heterogeneous population, num- ber and formation of strata, sample selection, estimators (total, mean, proportion), variances of the estimators, estimators for the variances, di erent allocation techniques, comparison with SRS, design e ect and its uses, poststrati cation, quota sampling. Auxiliary information in estimation: ratio estimators (total, mean), di erent properties: un- biasedness, variance (approximate), estimated variance, con dence interval, comparison with mean per unit estimates, conditions for best linear unbiased ratio estimator, application in strati ed sampling, unbiased ratio-type estimates; product estimator; regression estimator: linear regression estimate and its properties (unbiasedness, variance and estimated variance) under preassigned b and estimated b, comparison with mean per unit estimate, application in strati ed sampling, relative merits and demerits. Cluster sampling: motivation and reasoning, formation and size of clusters; cluster sampling with equal sized clusters: estimators and their various properties (unbiasedness, variance and estimated variance), comparison with SRS and systematic sampling, optimum cluster size, strati cation in cluster sampling: estimation and comparison with simpler sampling designs. Concept of design e ect, non-response and coverage rate, use of sampling weights.

Course Credit: 3

Course Description: The objectives of the course are to develop an understanding of the core ideas and concepts of numerical methods, to enable students to apply rigorous analytic and highly numerate approaches, and to develop scienti c computer programs and to equip students with the ability to apply Fourier series and Fourier integrals to signi cant applied problems, particularly in telecommunication, which are closely related to Laplace transform. Course Objectives: The objectives of the course are: To develop an understanding of the core ideas and concepts of numerical methods. To enable students to apply rigorous analytic and highly numerate approaches, and to develop scienti c computer programs. To equip students with the ability to apply Fourier series and Fourier integrals to signi cant applied problems, particularly in telecommunication, which are closely related to Laplace transform.Learning Outcomes Upon completion of the course, students will be able to CLO1 Understand and explain the theoretical foundations and concepts of numerical methods, including interpolation, numerical integration, and solutions of algebraic and transcendental equations CLO2 Analyze and solve real-life problems using Fourier series and Laplace transform techniques, and draw connections among these ideas CLO3 Evaluate the e ectiveness of di erent numerical methods and justify the use of speci c techniques for solving mathematical problems CLO4 Apply rigorous analytical approaches and develop scienti c computer programs to implement numerical methods CLO5 Create and present solutions to complex applied problems using Fourier and Laplace transforms, and demonstrate their application in telecommunication and other fields. Contents Interpolation and inverse interpolation: uses of Newton's forward and backward interpo- lation formula; Lagrange's formula; numerical integration: Simpson's rule; Weddle's rule; trapezoidal rule; Gauss's quadratic formulae and proper examples from the applications to econometrics, meteorology and biomedicine; Euler's formula of summation and quadrature. Solution of numerical algebraic and transcendental equations; equations in one unknown; nding approximate values of the roots; nding roots by repeated application of location theorem; method of interpolation or of false position; solution by repeated plotting on a large scale; Newton-Raphson method; Newton-Raphson method for simultaneous equations. Fourier series: periodic function; Fourier series process of determining the Fourier coe cients; Dirichlet conditions; odd and even functions; half range Fourier sine or cosine series; Parseval's identity; di erentiation and integration of Fourier series. Laplace transform: introduction; de nition of integral transformation; de nition of Laplace transform; Laplace transform of some elementary functions; su cient conditions for the exis- tence of Laplace transform; some important properties of Laplace transform; initial and nal value theorem; Laplace transforms of some special functions. Inverse Laplace transform: de nition of inverse Laplace transform; Lerch's theorem; some important properties of the inverse Laplace transform; partial function decompositions; def- inition of convolution; convolution theorem; Heaviside's expansion formula; evaluation of integrals; application of Laplace transform. Introduction to Taylor's and Laurent series.

Course Credit: 3

Course Description Graduate students in applied statistics need to know mathematical analysis. Real numbers, sets, intervals, sequences and series, limits, di erentiability, continuity, integration, measure theory, and probability are all covered in this subject. Prerequisites for this study include a basic mathematical science course called calculus. Course Objectives The course has great value for a student who wishes to go beyond the routine techniques to solve standard problems, and who wants to extend ideas to a new context. It develops the ability to analyze mathematical situations properly and precisely. It also helps the students to learn how to work comfortably with concepts that initially seemed so mysterious. Learning Outcomes Upon successful completion of the course, the students are expected to CLO1 Develop the ability to analyze mathematical situations properly and precisely. CLO2 Learn to work comfortably with concepts that initially seemed so mysterious. CLO3 Know real numbers, sets, intervals; sequences and series of real numbers and their convergence and divergence; Metric space and topological space and their proper- ties; di erent properties of limits, continuity, di erentiability and Rieman integral of a function. CLO4 Basic concepts of measure theory and probability measure and to relate them in real data scenarios Contents The real number system; axioms and completeness and its consequences; Dedekind cut, sets, compact sets; simple operation on them. Sequence of functions of one and several variables; limit; continuity; continuous functions; uniform continuity; di erentiation and integration; in nite series of constants and functions; convergence and divergence; power series: di erentiation and integration of power series; Taylor expansion with remainder or in in nite series. Metric and topological spaces; limit points; open and closed sets; interior and exterior points; boundary points; continuous mapping and Cauchy sequences. Measure and integrals on abstract sets on real lines; Cramer measurability: fundamental de nitions; auxiliary lemma; fundamental theorems; measurable functions; Lebesgue measure on a real line, plane; integrals; Riemann-Steiljes integrals.

Course Credit: 2

Course Description: Any scienti c task without the knowledge of software is di cult to imagine and complete in the current scenario. R is a free software that is capable of handling mathematical and statistical manipulations. It has its own programming language as well as built-in functions to perform any specialized task. Students intend to learn the basics of R software in this course. Course Objectives: The objective of the course are to teach the basics of R programming language that includes understanding di erent types of R objects, writing functions, reading/writing data of di erent formats, basic programming tools, and creating di erent types of plots. Learning Outcomes: After completion of the course students are expected to CLO1 be able to learn the basics of R programming language that includes understanding di erent types of R objects CLO2 understand the concepts of R functions, reading/writing data of di erent formats CLO3 able to use di erent data analysis tools, such as joining two data tables, subsetting from a data table, obtaining summary statistics, etc. CLO4 to create di erent types of plots using R functions

Course Credit: 2

Course Description: This course is designed to introduce computational methods and simulation techniques which that will be helpful for understanding theoretical concepts and practical applications of prob- ability and sampling distributions, and statistical inference including point and interval esti- mation and test of hypotheses. R programming is used to demonstrate related simulations and computations. Course Objectives: The main objective of this course is to introduce students to the theory of simulation and illustrate to them the theoretical concepts of sampling distributions and statistical inference using computer-simulated data. The course also aims at introducing students to compu- tational methods and statistical software (R programming) required for tting probability distributions, conducting point and interval estimation, and performing test of hypotheses using real-life datasets. Learning Outcomes Upon completion of the course, students are expected to CLO1 acquire detailed theoretical and practical knowledge of common techniques of sim- ulating data CLO2 write computer (R programming) codes for simulating data from di erent proba- bility distributions and di erent resampling techniques. CLO3 use simulated data to demonstrate theoretical concepts related to sampling distri- butions and statistical inference. CLO4 apply computational methods required for tting probability distributions, con- ducting point and interval estimation, and performing test of hypothesis using real-life data. CLO5 demonstrate skills to provide data-drive solution to inferential problems, interpret ndings from computational analysis and explain them to researchers from various disciplines and to practitioners working industries Contents Concepts of simulation and its uses in statistics; random number generations: congruential generators, seeding; random variate generations: inversion method (direct method), rejection method (indirect method); Monte-Carlo integration: hit-and-miss method, improved Monte- Carlo integration; variance reduction: antithetic sampling, importance sampling, control vari- ates. Use of simulated, repeated sampling and real datasets for illustrating theoretical and practical aspects of tting probability distributions, sampling distributions, point and interval estimation, and tests of hypotheses.

Course Credit: 2

Course Description: This computing course will discuss the applications of the statistical methods discussed in the courses design of experiment and demography. In addition, this course demonstrates the use of statistical software R to apply the models related to di erent experimental designs to analyze the data in the eld of agriculture, industry, and medicine. Moreover, this course helps students to learn, analyze and interpret real-life demographic data. Course Objectives: The course's main objective is to teach students to use statistical software (e.g., R) and analyze experimental design and demographic data. The speci c objective is to provide hands on learning by incorporating practical exercises and real-world examples to equip students with the knowledge and skills needed to excel in conducting scienti c research or working in industry. Learning Outcomes Upon completion of the course, students will be able to CLO1 have a solid understanding of the use of statistical software, e.g., R, and methods to analyze data in the area of experimental design and demography CLO2 learn how to apply the models related to di erent experimental designs (CRD, RBD, BIBD) to analyze the data in the eld of agriculture, industry, and medicine CLO3 learn to analyze and interpret demographic data, gaining insights into population trends, age-sex structures, fertility, mortality, migration, population projections and population growth rates CLO4 be equipped with the skills to write programs to obtain statistical results from data in the relevant eld and draw meaningful conclusions from statistical analyses, which are essential for informed decision-making in various elds for public policy and planning. Contents Practical problems and numerical exercises related to design of experiments, including com- pletely randomized design (CRD), randomized complete block design (RCBD), Latin square design (LSD), balanced incomplete block design (BIBD); construction of experimental layouts; estimation of treatment and block e ects; analysis of variance (ANOVA), and interpretation of results. Computation of demographic measures, including basic measures (masculinity proportions, sex ratio, age-child ratio, age dependency ratio), fertility indicators (crude birth rate, gen- eral fertility rate, age-speci c fertility rate, total fertility rate, gross reproduction rate, net reproduction rate), mortality indicators (crude death rate, age-speci c death rate, infant mor- tality rate, neonatal mortality rate, child mortality rate, direct and indirect standardization of mortality rates), and construction of population pyramid. Practical construction of life tables using standard approaches, including Fargany method; step-by-step calculation and interpretation of life table columns and functions and their real- world applications.

Course Credit: 2

Each student must be examined by a committee of selected members at the end of the aca- demic year.

Course Credit: 4

Course DescriptionF: This course explores the concepts and techniques involved in factorial design. It covers how to design factorial experiments, conduct them, and analyze the resulting data. Additionally, the course addresses experiments with random factors, as well as nested and split-plot designs. Course Objectives: The main objectives of the course are to teach the basic ideas of factorial design; design experiments involving up to 2 and 3 factors with k levels; analyze the data from such exper- iments; interpret the results of any analysis; and design and analyze experiments involving random factors. Additionally, the course aims to teach the methods involved in designing and analyzing experiments with k factors, each having two levels and three levels. Learning Outcomes: After completion of the course, students are expected to CLO1 understand the concept of factorial designs and design experiments involving up to two or three factors with k levels. CLO2 understand the concept of blocking and confounding in designs involving k factors with two levels. CLO3 understand the design and analysis of fractional factorial experiments for k factors, each with two levels, as well as experiments involving random factors. CLO4 develop skills to analyze the data produced from various experimental designs. CLO5 demonstrate skills in designing and implementing proper factorial experiments and explaining them to various stakeholders across di erent sectors. Contents Introduction to factorial designs: basic de nition and principles; advantage of factorials; two- factor factorial design; statistical analysis of xed e ects model, model adequacy checking,estimating model parameters, choice of sample size, assumption of no interaction in a two- factor model, one observation per cell; general factorial design; tting response curve and surfaces; blocking in a factorial design. 2k factorial design: introduction; 22 design; 23 design; general 2k design; a single replicate in 2k factorial design; blocking in a 2k factorial design; confounding in 2k factorial design; confounding in 2k factorial design in two blocks; confounding in 2k factorial design in four blocks; confounding in 2k factorial design in 2p blocks; partial confounding. Two-level fractional factorial designs: one-half fraction of 2k design; one-quarter fraction of 2k design; general 2k?p fractional factorial design; resolution III designs; resolution IV and V designs. Three-level and mixed-level factorial and fractional factorial designs: 3k factorial design, confounding in 3k factorial design, fractional replication of 3k factorial design, factorials with mixed levels. Response surface methods: introduction to response surface methodology; method of steepest ascent; analysis of second-order response surface; experimental designs for tting response surfaces; mixture experiments; robust designs. Experiments with random factors: random e ects model; two-factor factorial with random factors; two-factor mixed model; sample size determination with random e ects; rules for expected mean squares; approximate F tests; approximate con dence intervals on variance components; modi ed large-sample method; maximum likelihood estimation of variance com- ponents. Nested and split-plot designs: two-stage nested designs; statistical analysis, diagnostic check- ing, variance components; general m-staged nested design; designs with both nested and fac- torial factors; split-plot design; split-plot designs with more than two factors; split-split-plot design, strip-split-plot design.

Course Credit: 3

Course Description The main objectives of this course is to acquaint students with the methodologies associated with the advanced sampling techniques. This course introduces advanced sampling methods used in sample survey. It covers sampling of unequal clusters, two-stage sampling, multistage sampling, methods for estimating variance in complex surveys, and non-sampling errors.Course Objectives To acquaint students with the methodologies associated with the advanced sampling tech- niques and their application in real survey. Learning Outcomes Upon completion of the course, students are expected to be able to CLO1 understand the concept of a di erent sampling methods CLO2 gain knowledge about di erent multistage sampling, methods for estimating vari- ance in complex surveys and non-sampling error and their practical uses in large scale survey. CLO3 understand the methods of estimating the population characteristics of interest under di erent sampling scheme. CLO4 develop skills to determine the required sample size and calculate parameters under di erent sampling scheme. CLO5 demonstrate skills for designing and implementing a standard sample survey and explaining it to di erent stakeholders in many sectors.Contents Probability proportional to size (PPS) sampling: motivating examples, with replacement (WR) sampling: cumulative measure of size method and Lahiri's method, Hansen-Hurwitz (H-H) estimator (unbiasedness, variances, estimated variance), comparison with SRS, opti- mum measure of size, PPS without replacement (WOR) sampling: challenges and solutions, initial probabilities, normalizing probabilities, inclusion probabilities and their relation with the sample size, Horvitz-Thompson (H-T) estimator (unbiasedness, variance, estimated vari- ance), di erent methods of PPSWOR: Brewer's method, Durbin's method, Des Raj method, Murthy's method, Rao- Hartley-Cochran method, Multinomial distribution for PPSWR sam- pling, H-T estimator in case of PPSWR sampling. Sub-sampling, sub-sampling of unequal sized clusters: di erent estimators and their variances, two-stage sampling: design, estimators (total, mean), variances and their unbiased estimators, three stage sampling: design, estimators (total, mean), variances and their estimators, general framework (two-stage and three-stage) for estimating population total, di erent sampling designs at di erent stages, determination of sample sizes in two and three-stage sampling, optimum sampling and sub-sampling fractions, use of information from pilot survey.Concept of double sampling and its necessity, application in strati ed sampling, and in Ratio and Regression estimators, repeated sampling from the same population: sampling on two and more than two occasions. Complex survey: de nition and challenges involved in complex surveys, approaches of variance estimation (VE), replication methods for VE: random group method, balanced repeated repli- cation (balanced half-sample replication) method, Jackknife method and Bootstrap method, implementation of replication methods in complex sampling designs, post-strati cation. Non-sampling errors: sources of the errors, e ects of nonresponse, inference on population pro- portion in presence of nonresponse, types of nonresponse, Call-backs and its e ects, Hansen and Hurwitz approach for nonresponse, Politz-Simmons adjustment for bias reduction, math- ematical model for errors of measurement, mechanism of nonresponse, imputation and its di erent techniques. Special sampling designs: multiplicity, network sampling: design and estimation (multiplicity and Horvitz-Thompson estimators for population total, and their di erent properties), adap- tive sampling: adaptive cluster sampling (ACS) and related concepts used in ACS, Hansen- Hurwitz and Horvitz-Thompson estimators for population total, and their di erent properties.

Course Credit: 4

Course Description: This introductory course provides an overview of di erent types of regression and describes the use of linear regression. This course covers the theory underlying regression analysis, simple and multiple linear regression, classical estimation and testing methods, and residual analysis. In addition, it includes the formulation, analysis, interpretation and validation of linear regression models as well as the practical application of a statistical package to demonstrate how the theory can be applied to address a particular research question. Course Objectives Students are expected to learn the techniques of linear regression models and they should understand applications of the linear regression models in real life situations. Course Learning Outcomes (CLOs) After completion of this course, students are expected to CLO1 understand (explain ideas and concepts) Students will be able to explain the theory underlying regression analysis, including simple and multiple linear regression, and classical estimation and testing methods. CLO2 analyze (draw connection among ideas) Students will be able to analyze residuals and interpret the results of linear regression models. CLO3 evaluate (justify a stand or decision) Students will be able to evaluate the validity and accuracy of linear regression models using statistical testing methods. CLO4 apply (use information in new situation) Students will be able to formulate and apply linear regression models to solve real-life problems using statistical packages such as STATA or R. CLO5 create (produce a new or original work) Students will be able to create and validate new linear regression models to address speci c research questions. Contents Measures of association for quantitative data: correlation and inference concerning correlation; regression and model building, motivating examples, uses of regression. Simple linear regression model: model for E(Y jx), least squares estimation, assumptions related to errors, maximum likelihood estimation (MLE) of model, sampling distribution of MLEs of the model parameters, inferences concerning the model parameters (con dence intervals and t-test), con dence interval estimate of the E(Y jx) (con dence band). Model accuracy and diagnostics: goodness of t test (F-test, coe cient of determination, R2); prediction and prediction interval for a new Y at speci c x, residual analysis: de nition, normal probability plot, plots of residuals versus tted values, residuals versus x, other residual plots, statistical tests on residuals; detection and treatment of outliers; concept of lack of t and pure error, test for lack of t, transformations as solution to problems with the model, weighted least squares. Matrix representation of simple linear regression model, inference and prediction. Multiple linear regression models: formulation of multiple regression models, estimation of the model parameters: least squares estimation, maximum likelihood estimation, sampling distributions of the MLEs, con dence interval and hypothesis testing for concerning model parameters; model accuracy and diagnostics: goodness of t test (F test, R2, adjusted R2), prediction of a new observation; extra sum of squares principles and its application in test- ing general linear hypothesis, checking all assumptions concerning model and use of remedy measures when assumptions are not valid, detection and treatment of outliers, in uential observations. Polynomial regression model: introduction; polynomial models in one variable: basic prin- ciples, piecewise polynomial tting; polynomial models in two or more variables; orthogonal polynomials. Indicator variables: the general concept of an indicator variable, use of the indicator variables in linear regression, models with only indicator variables, idea of regression models with an indicator response variable. Variable selection and model building: the model building problem, consequences of model mis-speci cation, criteria for evaluating subset regression models, computational techniques for variable selection. Validation of regression models: concept, cross validation.

Course Credit: 3

Course Descriptions: This course serves as an introduction to epidemiology, the study of the distribution and de- terminants of health-related states or events in populations, and the application of this study to control health problems. Epidemiology is a cornerstone of public health, providing essen- tial tools for understanding disease patterns and developing e ective interventions. Topics include measures of disease occurrence, study designs, exposure-disease relationship, control of extraneous factors and interaction. Course Objectives: The course aims to equip students with the knowledge, skills and abilities necessary to under- stand disease patterns, identify risk factors, and contribute to evidence-based decision-making in public health and healthcare settings. It also emphasizes critical thinking, problem-solving, and ethical conduct in epidemiological research and practice. Learning Outcomes After completion of the course, the students are expected to CLO1 understand the basic principles and concepts of epidemiology CLO2 learn key epidemiological study designs and methods CLO3 develop skills in analyzing and interpreting epidemiological data CLO4 learn strategies to minimize bias and confounding in study design and analysis CLO5 learn the application of epidemiological ndings in developing public health inter- ventions and policies Contents Introduction: disease processes, statistical approaches to epidemiological data, study design, binary outcome data, causality. Measures of disease occurrence: prevalence and incidence, disease rates, hazard function; review of simple random samples, probability, conditional probabilities, and independence of two events. Measures of disease-exposure association: relative risk, odds ratio, relative hazard, risk, at- tributable risk. Study designs: population-based studies, cohort studies, case-control studies, case-cohort studies; Assessing signi cance of 2 2 tables obtained from chohort designs, case-control designs. Estimation and inference for measures of assocaition: odds ratio, sampling distribution and con dence interval for odds ratio, relative risk, excess risk, attributable risk. Confounding and interaction: causal inference, counterfactuals, confounding variables, control of confounding variables by strati cation, causal graphs, controllong confounding in causal graphs; Cochran-Mantel-Haenszel test, summary estimates and con dence intervals for odds ratio and relative risk after adjusting for confounding factors. Interaction: multiplicative and additive interaction, interaction and counterfactuals, test of consistency of association across strata, overall test of association, a test for trend in risk. Introduction to matching, types of matching, and analysis of matched studies.

Course Credit: 3

Course Descriptionf: This course deals with the analysis of time-to-event data (also known as survival or failure time data), which are commonly encountered in scienti c investigations. It is being exten- sively used in medicine, clinical trials, biological and epidemiological studies, engineering, economics, and social sciences. This course provides an opportunity for students to learn life- time probability distributions that are useful for modeling tine-to-event data. Topics include lifetime distributions and non-parametric and parametric approaches for analyzing time-to- event data. Course Objectives: The course's primary focus is to make students familiar with the situation where censored data appear and to be able to analyze such data by implementing appropriate methods and models. Secondly, to introduce statistical theory and methodology for analyzing lifetime data obtained from censored samples, emphasizing statistical lifetime distributions, types of censoring, graphical techniques, and non-parametric/parametric estimation. Learning Outcomes: After successful completion of the course, students are expected to CLO1 understand the basic features of censored lifetime data, survival function, and hazard functions CLO2 to learn di erent properties of lifetime distributions CLO3 to understand the use of location-scale and log-location scale families of ditributions in the analysis time-to-event data and learn its properties CLO4 understand di erent non-parametric methods for estimating survivor and hazard functions and corresponding inferences CLO5 understand parametric estimation methods for survival and hazard functions and corresponding inferences CLO6 be able to communicate conclusions obtained from time-to-event data analysis with researchers of related elds and policymakers. Contents: Basic concepts and models: lifetime distributions - continuous models, discrete models, a general formulation; some important models - exponential, Weibull, log-normal, log-logistic, gamma distributions, log-location-scale models, inverse Gaussian distributions, mixture mod- els; regression models. Observation schemes, censoring, and likelihood: right censoring and maximum likelihood; other types of incomplete data; truncation and selection e ects; information and design issues. Nonparametric and graphical procedures: nonparametric estimation of survivor function and quantiles; descriptive and diagnostic plots; estimation of hazard or density functions; methods of truncated and interval censored data; life tables. Inference procedures for parametric mod- els: inference procedures for exponential distributions; gamma distributions; inverse Gaussian distributions; grouped, interval censored, or truncated data; mixture models; threshold pa- rameters; prediction intervals. Inference procedure for log-location-scale distributions: inference for location-scale distri- butions; Weibull and extreme-value distributions; log-normal and log-logistic distributions; comparison of distributions; models with additional shape parameters; planning experiment for life tests.

Course Credit: 3

Course Description: To infer means to make general statements based on speci c observations. This is a task undertaken in almost every quantitative eld of research. This course deals with the advanced statistical inferential methods. It emphasizes concepts, methods and theory covering the broad topics of hypothesis testing, data reduction, likelihood inference in exponential families, and criteria for comparison of estimators. Successful completion of this course will provide a foundation for understanding probability-based statistical inference material presented in other courses. Course Objectives: The objective of this course is to provide a thorough theoretical grounding and working knowledge of statistical inference. It aims to teach fundamental materials which will be of use in specialized courses in statistics such as actuarial science and biostatistics. At the end of this course, one should be able to perform hypothesis tests, explain the principles of data reduction, judge the quality of estimators as well as choose appropriate methods of inference to tackle real problems. Learning Outcomes: After completion of the course, students are expected to CLO1 Provide a thorough theoretical grounding and working knowledge of statistical inference, including understanding the concepts of su ciency, ancillarity, and com- pleteness, and their roles in designing estimators. CLO2 Choose appropriate methods of inference to tackle real problems. CLO3 Judge the quality of estimators and compare between estimators based on di erent criteria. CLO4 Perform hypothesis tests with optimal properties and design hypothesis tests, and choose appropriate methods of inference to tackle real problems. CLO5 Perform hypothesis tests with optimal properties and design hypothesis tests. Contents: Statistical inference: parametric, nonparametric, and semiparametric inference. Approximate and computationally intensive methods for statistical inference: the general problem of inference; likelihood functions; maximum likelihood estimation; optimization techniques-Newton type methods; EM algorithm-simple form, properties, uses in analyzing missing data, tting mixture models and latent variable model; restricted maximum likelihood (REML) method of estimation; Multi-stage maximization; E cient maximization via pro le likelihood; con dence interval and testing hypothesis in these complex cases. Bayesian method of inference: prior and posterior distribution, di erent types of prior, cred- ible intervals and testing hypothesis; analytical approximations - asymptotic theory, Laplace approximation; numerical integral methods - Newton-Cotes type methods; Monte-carlo meth- ods; simulation methods - Markov chain Monte Carlo. Exact tests: test for single proportion and comparison of two proportions. Resampling techniques: bootstrap-con dence intervals, test, parametric bootstrap, advan- tages and disadvantages of parametric bootstrap; jackknife-con dence interval, test, and per- mutation test. Nonparametric inference and robustness: introduction, inference concerning cumulative distri- bution function (cdf), quantiles and statistical functionals: empirical cdf, quantiles, estimating statistical functionals, in uence functions, testing statistical hypothesis-one sample settings, two or more sample settings; tolerance limit; empirical density estimation- histograms, kernel, kernel density estimation.

Course Credit: 3

Course Description: The course provides a deeper knowledge within multivariate statistics, both in theory and applications. Multivariate distributions with emphasis on the multivariate normal distribution and its properties are considered. The course also provides deeper studies of the inference theory in multivariate analysis, for example concerning the mean and covariance matrices. The concepts that are more thoroughly treated in the course are: multivariate analysis of variance, pro le analysis, multivariate regression analysis. Matrix algebra is used through the course as a necessary tool for the inference as well as computer sessions. An overview about necessary concepts from matrix algebra useful for the course will be given. Course Objectives Multivariate data analysis helps in the reduction and simpli cation of data as much as possible without losing any important details. As MVA has multiple variables, the variables are grouped and sorted on the basis of their unique features. The variables in multivariate data analysis could be dependent or independent. It is important to verify the collected data and analyze the state of the variables. In multivariate data analysis, it is very important to understand the relationship between all the variables and predict the behavior of the variables based on observations. It is tested to create a statistical hypothesis based on the parameters of multivariate data. This testing is carried out to determine whether or not the assumptions are true. Learning Outcomes: After completion of the course, students are expected to CLO1 appreciate the range of multivariate techniques available, CLO2 be able to summarize and interpret multivariate data CLO3 have an understanding of the link between multivariate techniques and correspond- ing univariate techniques CLO4 be able to use multivariate techniques appropriately, undertake multivariate hy- pothesis tests, and draw appropriate conclusions. CLO5 know how to analyse several real life data in business, economics, Demography, Public Health, and medical data etc. using through multivariate techniques. Contents Preliminaries of multivariate analysis: applications of multivariate techniques; the organiza- tion of data; data display and pictorial representations; distance. Random vectors and random sampling: some basics of matrix and vector algebra; positive de nite matrices; a square-root matrix; random vectors and matrices; mean vectors and co- variance matrices; matrix inequalities and maximization; the geometry of the sample; random sample and expected values of sample means and covariance matrix; generalized variance; sample mean, covariance, and correlation as matrix operations; sample values of linear com- binations of variables. The multivariate normal distribution: the multivariate normal density and its properties; sam- pling from a multivariate normal distribution and maximum likelihood estimation; sampling distribution and large sample behavior of sample mean vector and sample variance-covariance matrix; assessing the assumption of normality; detecting outliers and data cleaning; transfor- mation to near normality. Inferences about a mean vector: the plausibility of mean vector as a value for a normal pop- ulation mean; Hotelling T2 and likelihood ratio tests; con dence regions and simultaneous comparisons of component means; large sample inference about a population mean vector; inferences about mean vectors when some observations are missing; time dependence in mul- tivariate data. Comparisons of several multivariate means: paired comparisons and a repeated measures design; comparing mean vectors from two populations; comparison of several multivariate population means (one-way MANOVA); simultaneous con dence intervals for treatment ef- fects; two-way multivariate analysis of variance; pro les analysis; repeated measures designs and growth curves. Multivariate linear regression models: the classical linear regression model; least squares esti- mation; inferences about regression model; inferences from the estimated regression function; model checking; multivariate multiple regression; comparing two formulations of the regression model; multiple regression model with time dependent errors.

Course Credit: 3

Course Description: The research methodology course is fundamental to teaching students the theoretical and practical skills required to conduct research in various elds. The course introduces students to the fundamental principles of research design, data collection, data analysis, and report writing. It will cover a range of research approaches, including quantitative, qualitative, and mixed methods. Course Objectives: The course aims to provide students with hands-on experience in designing and conducting research studies, particularly to develop students' knowledge and understanding of how to formulate research questions, develop hypotheses, choose appropriate research methods, and collect and analyze data and write a report for scienti c publication. In addition, the course is designed to provide students with the knowledge and skills necessary to conduct valid, reliable, and ethical research. Learning Outcomes After completion of the course, students are expected to CLO1 formulate research questions, develop hypotheses, choose appropriate research meth- ods, and collect and analyze data CLO2 learn about the various data collection techniques, such as surveys, interviews, observations, and statistical techniques for analyzing data CLO3 apply their knowledge through practical exercises CLO4 become competent in planning, conducting, evaluating, and presenting a research project CLO5 learn ethics-ethical issues, citation, acknowledgment, plagiarism, reproducibility, and accountability. Contents Foundations of Research: Meaning, concept, motivation, and objectives of the research; Types of research { descriptive vs. analytical, applied vs. fundamental, quantitative vs. qualitative, conceptual vs. empirical, concept of the applied and basic research process. Criteria and steps of good research. Language of research: Variables and attributes; concepts and constructs; theory and models; proposition and hypotheses: relational terminologies: independent and dependent variables, intervening variables, extraneous variables, moderating variables confounder variables. Problem Identi cation and Formulation: De ning and formulating the research problem, the importance of literature review in de ning a problem, identifying gap areas from literature and research database, research question, and formulation of research hypothesis. Research Design and Methods: Research methods vs. methodology; features of a good re- search design, concept, types, and uses of exploratory, descriptive, and experimental research designs. Qualitative and quantitative research approach, mixed methods design. Concept of measurement, problems in measurement in research - validity, and reliability. Sampling: use of sampling techniques in research design; brief review of sampling and sample size determi- nation. Techniques of data collection: Qualitative approaches { focus group discussion (FGD), in- depth interview (IDI), key informant interview (KII) and their guidelines and checklist; concepts of ethnography, content analysis, and discourse analysis, Quantitative approach { the concept of a survey, mode of a survey { face-to-face interview, telephone interview, online/email, etc. Survey tools { Questionnaire, schedule, structured, semi-structured, open- ended, and close-ended questions. Data collection apps: survey CTO, Kobo Toolbox, etc.; Field Implementation { a pilot study, monitoring the data collection, quality control, and data validity. Monitoring and Evaluation (M&E): Concept of monitoring and evaluation, objectives of M&E; performance monitoring versus performance evaluation. Key steps of M&E; M&E design: Baseline, ongoing, and end-line evaluation; evaluation criteria{relevance, e ectiveness, e - ciency, impact, and sustainability. Human resources and budget in research: allocation of human resources, preparing a budget for research work. Data Analysis: Steps of data preparation and analysis; Guidelines for using secondary data for research: when, how, and why;Dissemination of Research ndings: Di erent Steps inWriting Report, Layout of the Research Report; E ective presentation, preparing articles for peer review. Research Ethics and Scholarly Publishing: Ethics-ethical issues, ethical committees (human and animal); IPR- intellectual property rights and patent law, commercialization, copyright, royalty; scholarly publishing concept and research paper design, citation, acknowledgment, plagiarism, reproducibility, and accountability. Experiential Learning Project: Group project and eld work { writing a research proposal, developing and implementing eld data collection, data analysis, and report writing and presentation.

Course Credit: 2

Course Description: This course is designed to provide students with a comprehensive understanding of using Stata-a powerful statistical software package-for data science applications. Students will learn how to leverage Stata's capabilities to explore, analyze, and visualize data, with a focus on practical skills relevant to data science and statistical analysis. Objectives: The objectives of the course are to empower students with practical Stata skills and analytical competencies essential for conducting data-driven research and making informed decisions in various academic, professional and research settings. The course emphasizes hands-on learning of data entry, management, analysis and e ective communication of findings. Learning Outcomes After completion of the course, the students are expected to CLO1 gain pro ciency in using Stata for data entry, manipulation, cleaning and transfor- mation CLO2 develop skills in data visualization and presentation of results CLO3 apply Stata for reproducible research CLO4 develop problem-solving skills by tackling data analysis challenges CLO5 apply statistical reasoning and Stata skills to address research questions and make data-driven decisions. Contents Introduction to Stata: di erent windows and les, help le and searching for information; data entry, reading both stata and other format of data le, use of command-import and export, combining stata les; example command{ append, merge, (1-to-1, 1-to-m); explor- ing data: example commands-browse, edit, list, sort, describe, assert, codebook; converting string variable to numeric: example command{encode, decode; changing data layout: example command-reshaping (wide-to-long, long-to-wide form); collapsing data. Data management: creating a new data set specifying subsets of data with in and if quali- ers, generating and replacing variables, using functions based on egen command, converting numeric and string formats, creating new categorical and ordinal variables, creating random data and random samples; matrix algorithm: formation, transpose, inverse, etc. Introduction to ado- le: creation and use of ado- le, foreach loops, and macro variables (local and global). Data summarization: graphs: example commands- histograms, scatterplots, line plots, connected- line plots, two-way plots, box plots, CI/forest plot, combining graphs; matrix plot, exploratory data analysis: summary statistics and tables: example commands - summarize, tabstat, ta- ble; frequency tables and two-way cross tabulations, multiple tables and multi-way cross tabulations, tables of means, medians and other summary statistics; one-sample mean and proportion test, two-sample mean test, con dence interval estimation; producing summary statistics for sub-group using stata command bysort; weighting observations and use of weight in producing summary statistics: example command{svy, aweight, iweight, fweight.

Course Credit: 2

Course Description: Python has become one of the most popular programming languages for data science due to its simplicity, versatility, and robust data analysis and machine learning capabilities. As organizations continue to digitize and generate increasingly large amounts of data, open- source tools like Python can enable data manipulation and exploration, machine learning, and statistical analysis in a scalable manner. This course provides a gentle introduction to programming in Python and its applications in data science and analytics. Objectives To give students a working knowledge of Python programming. To teach programming fun- damentals, basic data structures, writing functions, and importing and exporting data in di erent formats. To cover data manipulation and data visualization using Python. To pre- pare students for more advanced courses in data science and machine learning. Learning Outcomes Upon completion of CSE-530, students will be able to CLO1 Understand the fundamentals of Python programming, including basic syntax, data types, control structures, and functions (Concept, Computing). CLO2 Perform data analysis using NumPy and pandas, including data manipulation and exploratory data analysis (Application, Computing). CLO3 Create e ective data visualizations using matplotlib and seaborn (Application, Computing). CLO4 Produce dynamic statistical reports using interpreting and documenting visualiza- tions and analyses of real-world problems. (Communication, Collaboration). Contents Fundamentals of Python: Installing Python and Jupyter Notebook; the basic syntax of a Python program, Python data types; expressions and variables; lists, tuples, sets, and dictio- naries; writing conditions, loops, and functions. Data analysis with NumPy and pandas: installing NumPy and pandas, NumPy arrays; in- dexing, slicing, and iterating NumPy arrays; arithmetic and matrix operations with NumPy; pandas objects{ DataFrame, Series, and Index; data indexing and selection; handling missing data; combining and joining datasets, aggregation and grouping, exploratory data analysis. Data visualization with matplotlib and seaborn: Bar plots, histograms, density plots. boxplots and scatterplots.

Course Credit: 2

Course Description This statistical computing course provides a comprehensive understanding of applications of the methods covered in the courses design and analysis of experiments, epidemiology, and lifetime data analysis to real-life problems, equipping students with the tools and knowledge to address real-life problems across various elds. By achieving these skills, students are expected to make data-driven decisions and contribute to solving the complex challenges faced by society today. Course Objectives This course aims to equip students with the skill to use statistical software (e.g., R, Stata, or Python) to apply the methods discussed in the courses design and analysis of experiments, epidemiology, and lifetime data analysis. Through these skills, students are expected to tackle problem-solving challenges while working in industry, agency, or academia, make data-driven decisions, and contribute to planning and policy. Learning Outcomes After completion of the course, the students are expected to CLO1 understand how to use R, Stata or Python to linear models used in factorial ex- periments CLO2 to be able to perform analysis related to epidemiological studies CLO3 to be able to obtain non-parametric and parametric estimates of survival and cu- mulative hazards functions CLO4 able to interpret the statistical results for decision-making processes related to healthcare, engineering, nance, and more. Contents Analysis of factorial designs, screening experiments, split-plot designs, and response surfaces. Estimating odds ratio, risk ratio, and risk di erence for di erent types of study designs and corresponding inference. Estimating the survival function and cumulative hazards function using non-parametric and parametric methods.

Course Credit: 2

Course Description: This computing course is based on applications of regression models, multivariate methods, and statistical inference to real-life problems. By mastering these techniques for solving real- life problems, students will be equipped to analyze complex datasets, uncover meaningful insights, and contribute to data-driven decision-making processes in academia, industry, and research. Objectives: The objectives of this computing course are to teach students the applications of some sta- tistical methods (regression models, multivariate methods, and statistical inference) using statistical software (R, Python, or Stata) and interpret the results. More speci cally, the idea is to engage students in hands-on exercises and projects that involve real-life datasets, provid- ing practical experience in applying regression models, multivariate methods, and statistical inference techniques to address real-world problems. Learning Outcomes: After completion of the course, the students are expected to CLO1 understand the applications of linear regression models to real-life problems CLO2 perform parametric and nonparametric hypothesis tests and corresponding con - dence intervals CLO3 e ectively utilize statistical computing tools and software packages such as R, Stata, or Python to implement regression models, multivariate methods, and statistical inference techniques CLO4 manipulate and analyze large datasets, visualize results, and present their ndings clearly and concisely. Contents: Problems related to tting simple and multiple linear regression models, related inference, model diagnostics, and model selection; Exploratory analysis of multivariate data, multivari- ate tests, MANOVA and multivariate regression, hypothesis tests, con dence intervals, and bootstrap methods, and nonparametric tests.

Course Credit: 2

Each student must be examined by a committee of selected members at the end of the aca- demic year.

Course Credit: 3

Course Description: This module covers two important parts, one is advanced probability and another is stochastic processes. The module begins with a brief overview of modern probability and convergence of random variables and then moves on to the stochastic process to describe Markov chains, Poisson process, continuous time Markov chain and renewal process. Course Objectives: To develop a deep understanding of the advanced concepts in probability theory and stochastic processes. To apply these concepts to solve real-world problems in various domains. To pre- pare students for research and professional practice in elds requiring sophisticated stochastic modeling. Course Learning Outcomes (CLOs) Upon completion of the course, students will be able to CLO1 demonstrate advanced knowledge of probability theory and stochastic processes, including probability spaces, random variables, and convergence of random vari- ables CLO2 apply probability theory to model and analyze random experiments CLO3 solve complex probabilistic problems using Markov chains, Poisson processes, and renewal processes CLO4 develop skills to derive and prove theorems and lemmas related to probability theory and stochastic processes. CLO5 demonstrate skills to interpret the results obtained from stochastic modeling and provide recommendations. Contents Modern probability: events as sets, eld, sigma eld, probability measure, Borel eld and extension of probability measure, measure theoretic approach of random variables; probability space. Convergence of random variables: modes of convergence: almost sure, rth mean, in probabil- ity, in distribution, their interrelationship; law of large numbers, strong and weak laws of large numbers, limiting distribution; central limit theorem; law of iterated logarithm; martingale. Markov chains: introduction, Chapman-Kolmogorov equations, classi cation of states, lim- iting probabilities, gambler's ruin problem, mean time spent in transient states, branching processes, time reversible Markov chains, Markov chain Monte Carlo methods, Markov deci- sion processes, hidden Markov chains. Continuous-time Markov chains: introduction, continuous-time Markov chains, birth and death processes, transition probability function, limiting probabilities, time reversibility. Poisson process: exponential distribution, properties, convolutions of exponential random variables; counting processes, Poisson process, interarrival and waiting time distributions, further properties of Poisson processes, generalizations of the Poisson process, nonhomoge- neous Poisson process, compound Poisson process, conditional or mixed Poisson processes. Introduction to queueing theory: Classical M/M/1 queue, global and local balance, perfor- mance measures, Poisson arrivals see time averages (PASTA) property, M/M/1/S queueing systems, blocking probability, performance measures, multi-server systems { M/M/m, perfor- mance measures, waiting time distribution of M/M/m, performance measures of M/M/m/m with nite customer population, Erlang loss systems.

Course Credit: 4

Course Description: The course provides an introduction to the eld of Arti cial Intelligence and a broad but thorough introduction to the methods and practice of basic statistical machine learning and its core methods, models, and algorithms. This course is about providing students of ap- plied statistics and data science with detailed knowledge of how the basic Machine Learning methods work for arti cial intelligence and how statistical models can be brought to bear in computer systems not only to analyze large, high-dimensional, and big data sets but also to let computers perform tasks, that traditional methods of computer science are unable to address. Course Objectives: After completing the course students will be familiar with the concept of Arti cial Intelligence, Big Data, and their areas. It describes philosophies and techniques of Arti cial Intelligence, including intelligent agents, and search. It also describes several models for supervised and unsupervised machine learning and regularized modeling techniques, assess the strengths and weaknesses of each of these models, know the underlying mathematical relationships within and across statistical learning algorithms, develop and implement optimization methods for training of statistical models, design decision and optimal control problems to improve the per- formance of statistical learning algorithms, design and implement various statistical machine learning algorithms in real-world applications, evaluate the performance of various statisti- cal machine learning algorithms, demonstrate a working knowledge of dimension reduction techniques. identify and implement advanced computational methods in machine learning. Learning Outcomes After completion of the course, students are expected to CLO1 gain understanding of Arti cial Intelligence (AI), Machine Learning, Big Data, and their application areas. CLO2 be able to identify and describe several models for supervised and unsupervised machine learning, including regularized modeling techniques for AI. CLO3 develop skills to analyze, interpret, and predict data using various machine-learning methods based on various resampling techniques, with a particular focus on AI. CLO4 understand and explain the underlying mathematical relationships within and across statistical learning algorithms. CLO5 develop the ability to conduct comprehensive data analyses for high-dimensional data, including tting, diagnosing, and validating various machine learning models, to address real-world data challenges e ectively for AI. Contents Introduction to Arti cial Intelligence|De nition and History of AI, AI Applications and Impact on Society, Overview of AI Sub elds, Components of an AI system. Problem Solv- ing and Search|Problem Formulation, Uninformed Search Strategies: Breadth-First Search, Depth-First Search, Informed Search Strategies: Best-First Search, A* Algorithm. Overview of basic concepts and techniques of statistical machine learning, Data science con- cepts and their application areas. Overview of supervised and unsupervised learning. Overview of Big Data, including its de nition, sources, characteristics, and the challenges associated with processing and analyzing large datasets. Big data applications: examples and use cases. The Hadoop framework and its various components include HDFS, MapReduce, YARN, and Hive. Statistical learning: Statistical learning and regression, the curse of dimensionality and para- metric models, assessing model accuracy and bias-variance trade-o , classi cation problems, and K-nearest neighbors. Linear regression: Model selection and qualitative predictors, interactions, and nonlinearity. Classi cation: Introduction to classi cation, logistic regression, and maximum likelihood, multivariate logistic regression and confounding, case-control sampling and multiclass logistic regression, linear discriminant analysis and Bayes theorem, univariate linear discriminant analysis, multivariate linear discriminant analysis, and ROC curves, quadratic discriminant analysis and naive bayes. Resampling methods: Estimating prediction error and validation set approach, k-fold cross- validation, cross-validation- the right and wrong ways, the bootstrap, more on the bootstrap. Linear model selection and regularization: Linear model selection and best subset selection, forward stepwise selection, backward stepwise selection, estimating test error using Mallow's Cp, AIC, BIC, adjusted R-squared, estimating test error using cross-validation. Shrinkage methods: Ridge regression, Lasso, adaptive Lasso, Group Lasso, elastic net and adaptive elastic net, bridge, tuning parameter selection for ridge regression, lasso, and elastic net, total variation regularization. Dimension reduction and unsupervised machine learning techniques: Techniques to reduce the dimension of data, principal components and principal components regression and partial least squares. Clustering (K-means, Fuzzy C-means, Hierarchical Clustering). Introduction to Decision trees and Classi cation trees. Arti cial Intelligence and Statistical machine learning case studies in R and Python.

Course Credit: 3

Course Description: Multivariate analysis skills are recognized as part of the key requisites for statistical analysts. The complexity of most real-world phenomena requires investigators to collect and analyze observations on many di erent variables rather than a single variable. The need for statistical techniques to extract information from multivariate data thus becomes essential and crucial for data analysts. This course focuses on multivariate methods based on normal theory. It provides students with working knowledge on how to analyze data and solve problems involving measurements of p variables on each of n subjects. Course Objectives: The objective of this course is to provide students with experience in using multivariate techniques for analyzing research data. The aim is to teach students how to select appropriate methods for multivariate data analysis and interpret the results e ectively. Learning Outcomes After completion of the course, students are expected to CLO1 perform a principal components analysis, and interpret the principal component scores. CLO2 understand the concept of factor analysis, and di erent methods to estimate the parameters of a factor model; understand factor rotation, and interpret the rotated factor loadings. CLO3 perform a canonical correlation analysis, and interpret the canonical variate scores; CLO4 carry out cluster analysis, know how to partition the data into clusters of known composition. CLO5 demonstrate skills for implementing appropriate methods for multivariate data analysis, interpret the results, and explaining it to di erent stakeholders in many sectors. Contents Principal components: population principal components, summarizing sample variations by principal components, graphing the principal components, large sample inference.Factor analysis: the orthogonal factor models, methods of estimation (maximum likelihood estimates and principal factor analysis), selection of loadings and factor (factor rotation, varimax rotation, quartimax rotation, oblimin rotations), factor scores, structural equations models. Canonical correlation analysis: canonical variates and canonical correlations, sample canonical variates and sample canonical correlations, large sample inference. Discrimination and classi cation: separation and classi cation of two populations, classi - cation of two multivariate normal populations, evaluating classi cation functions, Fisher's discriminant function, classi cation with several populations, Fisher's method for discrimi- nating several populations. Clustering: similarity measures, hierarchical clustering methods, nonhierarchical clustering methods; fuzzy clustering, determination of number of clusters: Gap statistics and its several modi cations, several cluster validity indices, cluster's homogeneity test; multidimensional scaling.

Course Credit: 4

Course Description: This course covers a range of econometric methods required to conduct empirical economic research and understand applied econometric results. Topics include models for panel data, simultaneous equations models, models with lagged variables, and limited dependent variables. Course Objectives: The objectives of the course are to introduce students to the basic principles of econometric analysis; to help students gain theoretical understanding of the statistical models needed for econometric research including their underlying assumptions, advantages and limitations and to help them understand how to apply di erent econometric tools to analyze real-world economic problems and interpret findings. Learning Outcomes On successful completion of this course the students are expected to CLO1 understand the basic principles of econometric analysis and general steps for build- ing econometric models. CLO2 gain theoretical understanding of the statistical models needed for econometric research including underlying assumptions, sources and consequences of model mis- speci cations and comparative advantages and disadvantages of di erent models. CLO3 learn about methods for estimating econometric models from data. CLO4 apply di erent econometric tools to analyze real-world economic phenomena and problems. CLO5 demonstrate skills to summarize, interpret and explain results of econometric anal- yses.Contents Speci cation analysis and model building: estimation issues in the presence of perfect mul- ticollinearity and high but imperfect multicollinearity, detection and remedial measures of multicollinearity, OLS estimation in the presence of heteroscedasticity, method of general- ized least squares, consequences of using OLS in the presence of heteroscedasticity, detection and remedial measures of heteroscedasticity, OLS estimation in the presence of autocorrela- tion, detection and remedial measures of autocorrelation, types of speci cation errors, tests of speci cation errors (Durbin Watson test, Lagrange Multiplier test), consequences of errors of measurement, incorrect speci cation of the stochastic error term, bias caused by omission of relevant variables, inclusion of irrelevant variables; testing non-nested hypotheses, concept of encompassing model, and model selection criteria. Models for panel data: Panel data structure and advantages, constant coe cient model, xed e ects least square dummy variable model; xed e ect within group model; random e ect model, assumptions and estimation, comparison of xed e ect and random e ect models. Simultaneous equations models: nature of simultaneity and illustrative systems of equations, bias and inconsistency of OLS estimators, problem of identi cation, under-identi cation, exact-identi cation, and over-identi cation, rank and order conditions for identi cation, test of simultaneity, test of exogeneity, limited information estimation methods, estimation by OLS, instrumental variables (IV), Two-Stage Least Squares (2SLS), indirect least square (ILS), limited information maximum likelihood, full-information maximum likelihood, recur- sive systems and exactly identi ed equations. Models with lagged variables: lagged e ects in a dynamic model, lag and di erence oper- ators, nite distributed lag models, in nite lag model, Koyck approach to distributed lag models, estimation of the distributed lag model, adaptive expectations model, partial adjust- ment model, estimation of autoregressive model, detecting autocorrelation in autoregressive model, econometric forecasting, vector autoregressive models (VAR) forms and estimation, forecasting with VAR, testing for Granger causality. Models for limited dependent variable: linear probability model, logit model, grouped logit model, probit model, truncated regression model, censored regression model, Poisson regression models.

Course Credit: 3

Course Description: Lifetime data (also known as survival or failure time data) are commonly observed in health science, engineering, and social sciences. This course deals with di erent approaches of mod- eling lifetime data. The theoretical backgrounds and related practical applications of both parametric and semi-parametric approaches of analysing lifetime data are discussed in the course. A brief introduction to competing risks and frailty models is also provided. Course Objectives The course primarily focuses on familiarizing students with regression models commonly used to analyze time-to-event (lifetime) data. Both the accelerated failure time (AFT) model and Cox's proportional hazards (PH) model will be discussed in detail in the course. Students will also learn about the methods for analyzing competing risks models and correlated time- to-event data. Learning Outcomes: After completion of the course, students are expected to CLO1 understand the concepts related to regression models for time-to-event data in general CLO2 understand the theories related to accelerated failure time and proportional hazards model CLO3 develop skills to interpret the results obtained from regression models for time-to- event data. CLO4 understand the concepts of correlated time-to-event data and frailty models CLO5 understand the concepts of multiple mode of failures and di erent approaches of competing risks models Contents Parametric regression models: log-location-scale (Accelerated Failure Time) regression mod- els, proportional hazards regression models; graphical methods and model assessment; in- ference for log-location-scale models; extensions of log-location-scale models; hazard-based models. Semiparametric multiplicative hazards regression models: methods for continuous multiplica- tive hazards models - estimation and tests for regression parameter vector, comparison be- tween two or more lifetime distributions, justi cation, and properties of the likelihood func- tion, adjustment of tied lifetimes, estimation of baseline cumulative hazard function, strati - cation, time-varying covariates, model checking. Competing risks: introduction, hazard, and cumulative incidence function, modeling cause- speci c hazards and cause-speci c incidence. Frailty models: introduction to frailty, gamma frailty distributions, parametric frailty model, semi-parametric frailty model, and shared frailty model.

Course Credit: 3

Course Description: This course is designed to introduce key computational concepts, tools and techniques for cu- rating, managing, and analyzing data of large volume, various types and di erent frequencies. This course assumes basic exposure to the concepts of arti cial intelligence, machine learning algorithms, deep learning and computer programming. Course Objectives: The principal aim of this course is to introduce Big Data and its characteristics and challenges to students, and to teach them appropriate tools for managing and analyzing such large-scale data. Further objectives include helping students understand applications of Big Data in di erent elds and also ethical issues related to Big Data. Learning Outcomes After completion of the course, students are expected to CLO1 understand and describe the characteristics and challenges of Big Data. CLO2 identify and utilize appropriate tools for managing large-scale data. CLO3 understand and explain the underlying mathematical relationships within and across arti cial intelligence tools and to design and implement those tools for real- world applications. CLO4 develop computational skills for analyzing data of large volume, various types, and di erent frequencies. CLO5 recognize and evaluate ethical issues related to the use of Big Data. Contents Introduction to Big Data: de nition, characteristics and applications of Big Data in various elds. Data pre-processing: data collection and extraction { scraping data, data cleaning- handling missing values, noisy data and outliers; redundancy and correlation analysis, tuple duplication, con ict detection and resolution. Structured and unstructured data and databases - relational. and NoSQL databases. Data reduction{ overview, Wavelet transformation`, Attribute Subset Selection, Data Cube Aggregation; Data Transformation and Discretization. Introduction to Big Data Analytics: techniques to address data analysis issues related to data volume (Scalable and Distributed analysis), data velocity (High-Speed Data Streams), Data Variety (Complex, Heterogeneous, or Unstructured data), and Data Veracity (Data Uncertainty). Database management essentials for Big Data organization and manipulation: Introduction to data organization (lists, queues, priority queues, trees, graphs, hash). Basic graph models and algorithms for searching, shortest path algorithms, ow networks, matching. Processing and streaming Big Data, introduction to data architecture software including MapReduce, Hadoop distributed le system, Spark, Terradata, and how these tools work. Data Analysis and Visualization Techniques: Descriptive statistics, probabilistic modeling of Big Data (e.g., graphical models, latent variable models, hidden Markov models.) Bayesian Inference (e.g., variational inference, expectation propagation, sampling.) Bayesian Machine Learning (e.g., Bayesian linear regression). Fundamentals of data visualization, Infographics, layered grammar of graphics. Introduction to Modern, mosaic plots, parallel coordinate plots, introduction to GGobi data visualization system, linked plots, brushing, dynamic graphics, model visualization. Big Data Ethics and Privacy: Ethical considerations in data collection and analysis, privacy and security concerns in Big Data, legal and regulatory frameworks for Big Data.

Course Credit: 3

Course Description: This course serves as an introduction to time series theory. Its objective is to equip stu- dents with various classical time series models, including deriving their properties, inference methods, and forecasting techniques for analyzing time series data. From a computational standpoint, the course aims to demonstrate theory with real datasets. Conclusions and proofs are provided for some basic formulas and models to enable students to understand the prin- ciples of time series theory. Course Objectives: Upon completion of the course, students should become acquainted with the main concepts of time series theory and methods of analysis. They should understand the di erences be- tween cross-sections and time series and grasp the fundamental advantages and necessity of appropriate forecasting methods in particular environments. Additionally, students should be pro cient in using the statistical software R to analyze time series data. Learning Outcomes After completing the course, students are expected to CLO1 Understand the concept of time series analysis and be able to choose the most suitable analysis technique for the given data. CLO2 Have detailed knowledge of di erent time series techniques and the general steps for conducting and forecasting time series data. CLO3 Understand the methods for estimating the parameters of interest under di erent time series techniques. CLO4 Develop skills to forecast future observations and apply them in practice. CLO5 Demonstrate skills in designing and implementing a time series technique and ex- plaining it to stakeholders in various sectors.Contents Introduction and examples of time series; simple descriptive techniques: time series plots, trend, seasonal e ects, sample autocorrelation, correlogram, ltering. Probability models: stochastic processes, stationarity, second-order stationarity, white noise model, random walks, moving average (MA) processes, autoregressive (AR) processes, ARMA processes, seasonal ARMA processes, the general linear process; properties, estimation and model building, diagnostic checking. Forecasting: naive procedures, exponential smoothing, Holt-Winters, Box-Jenkins forecasting, linear prediction, forecasting from probability models. Non-stationary time series: non-stationarity in variance-logarithmic and power transforma- tions; non-stationarity in mean; deterministic trends; integrated time series; ARIMA and seasonal ARIMA models; modelling seasonality and trend with ARIMA models. Stationary processes in the frequency domain: the spectral density function, the periodogram, spectral analysis. Concept of state-space models: dynamic linear models and the Kalman lter.

Course Credit: 3

Course Description: This course is about introducing statistical methods including the general linear model for quantitative responses (including multiple regression, analysis of variance, and analysis of covariance), binomial regression models for binary data (including logistic regression and probit models), and models for count data (including Poisson regression and negative binomial models). All of these techniques are covered as special cases of the Generalized Linear Model, which provides a central unifying statistical framework for the entire course. Course Objectives: After completing the course students will be familiar with a uni ed procedure of several mod- eling techniques. They will be familiar with the exponential family of distributions, the class of generalized linear models (GLM) as regression models with responses from the exponential family of distributions, the concepts of link functions for modeling the correspondence between the expected value of the responses and covariates and of variance functions for specifying the correspondence between the expected values and variances of the responses, analyzing data from important special cases of GLMs, in particular logistic regression and Poisson regres- sion, and extensions of the GLM framework using quasi-likelihood based on speci ed link and variance functions. Learning Outcomes After completion of the course, students are expected to CLO1 gain a comprehensive understanding of the exponential family of distributions and their relevance to generalized linear models. CLO2 describe and apply the generalized linear models for both quantitative and quali- tative response variables within the GLM framework. CLO3 develop skills to analyze and interpret data using various special cases of GLMs, with a particular focus on logistic regression and Poisson regression. CLO4 extend the GLM framework using quasi-likelihood methods based on speci ed link and variance functions, allowing for exible modeling of complex data structures. CLO5 develop the ability to conduct comprehensive data analyses, including tting, diag- nosing, and validating various GLM models, to address real-world data challenges e ectively.Contents Generalized linear models: exponential family of distributions; estimation: method of maxi- mum likelihood, method of least squares, estimation of generalized linear models; inference: sampling distribution for scores, sampling distribution for maximum likelihood estimators, con dence intervals for model parameters, adequacy of a model, sampling distribution for log-likelihood statistic, log-likelihood ratio statistic (deviance), assessing goodness of t, hy- pothesis testing; multiple regression: maximum likelihood estimation, log-likelihood ratio statistic. Models for binary responses: probability distributions, generalized linear models, dose re- sponse models, general logistic regression, maximum likelihood estimation and log-likelihood ratio statistic, other criteria for goodness of t, least square methods; multinomial distribu- tions; nominal logistic regression models; ordinal logistic regression models. Models for count data, Poisson regression and log-linear models: probability distributions, maximum likelihood estimation, hypothesis testing and goodness of t.

Course Credit: 3

Course Description: O cial statistics is a branch of statistics that deals with the collection, analysis, interpretation, and dissemination of data produced by government agencies and other o cial bodies. Its purpose is to provide accurate and reliable information on various aspects of society, such as the economy, population, health, education, and crime. O cial statistics are used for various purposes, including policy-making, research, business-decision making etc. Course Objectives: The objectives of the course are to make students familiar with di erent sources of o cial statistics and their institutional, legal, and ethical aspects, and to prepare students with strong methodological basis for measuring, processing, producing, and using o cial statistics for national policies and planning. Course Learning Outcomes (CLOs) After completing this course, students are expected to CLO1 understand the fundamental concept of o cial statistics and their importance in practice CLO2 understand the methodological aspect of measuring, collecting and processing o - cial statistics CLO3 be familiar with the legale and ethical aspects of using o cial statistics CLO4 know in details about the di erent types and sources of o cial statistics and their use in practice CLO5 develop skills to demonstrate the use o cial statistics for nataional policies and planning and explain it with di erent stakeholders. Contents Domains of o cial statistics, concepts, de nitions, and statistical standards; fundamental principles of o cial statistics; code of practice of o cial statistics in Bangladesh; Legal and ethical framework for o cial statistics; Sector-speci c data quality assessment framework. Role of o cial statistics in monitoring the progress of global and national goals and policies. Data availability of the indicators of global and national goals and policies. Use of administrative data in o cial statistics: sources of administrative data, collection, process, and use of administrative data in o cial statistics. Use of survey data in o cial statistics; sources of surveys in Bangladesh; analysis of survey data for o cial statistics; use of survey weighting for o cial statistics. Demographic Statistics: Population growth, techniques to measure it, doubling time con- cept in demography; population estimates and projections; di erent techniques of population projection- component method, arithmetic/linear method, geometric method, exponential method, matrix method, Lee-Carter model, Bayesian model etc., for population projections. Health and well-being statistics: maternal and child health statistics, health services, general and chronic health statistics, health workforce. Macro-Economy Statistics: GDP, GDP per capita, GDP growth, In ation rate, Remittance etc. Business Economy Statistics: Short-and long-term business statistics; Science and tech- nology; Environment and energy; Transport and travel; Labour Force Statistics: Income and social conditions; Employment, unemployment, and earnings. Agricultural statistics: Food production and consumption (crop, forestry, and sheries), Food Balance Sheet, Food insecurity experience sclse (FIES), land use statistics, and climate and environmental statistics. Education statistics: Enrollment, dropout, completion, transition rates at di erent levels of education, teacher student ratio. National income: concepts and methods of measurement; social accounting matrix. Distribu- tion of income and wealth: Pareto and Lognormal distribution. Poverty: concept, steps in measurement. De ning poverty lines: subjective and objective poverty lines. Measures of poverty: headcount, gap, squared gap (Foster-Greer-Thorbecke), Sen, Sen-Shorrocks-Thon, Watts poverty indexes. Robustness of indexes: sampling error, measurement error. Poverty mapping, poverty comparisons. Vulnerability to poverty: mea- suring and quantifying vulnerability. The e ect of taxation on inequality and poverty. Mul- tidimensional poverty index.Inequality: concept, measurement of positive and normative measures; Lorenz curve; Gini co- e cient; Atkinson's index, Theil's index, Human development index. Inequality comparisons. Psychometry: concept, measurement; intelligent and achievement tests; z-score and t-score; intelligent quotient. O cial statistics for all SDG indicators; Data visualization and GIS mapping; time series of o cial statistics.

Course Credit: 2

Course Description: This course provides hands-on experience with di erent inferential procedures and multivari- ate techniques, focusing on their application to real-life problems. Students will learn to use statistical software (R package) to analyze data using principal component analysis, factor analysis, discriminant analysis, and canonical correlation analysis. The course aims to equip students with the skills necessary to interpret and present their ndings clearly. Course Objectives: The objectives of the course are to provide students with hands-on experience in applying di erent inferential procedures and multivariate techniques using statistical software (R pack- age).Teach students how to extract and present the most important features from complex data. Finally enable students to interpret analysis results and prepare scienti c publications. Learning Outcomes: Upon completion of the course, students will be able to CLO1 understand and explain the theoretical foundations and concepts of di erent multi- variate analysis techniques, including principal component analysis, factor analysis, discriminant analysis, and canonical correlation analysis. CLO2 analyze real-life data using multivariate techniques and inferential procedures, drawing connections among various ideas and concepts. CLO3 evaluate the results obtained from multivariate analysis, justify decisions, and write scienti c publications based on the analysis. CLO4 apply statistical software (R package) to perform multivariate analysis and solve real-life problems e ectively. CLO5 develop new or original work by implementing advanced multivariate techniques and presenting signi cant ndings clearly to stakeholders and researchers from other disciplines. Contents Problems related to Inference and Multivariate analysis: principal component analysis, fac- tor analysis, discriminant analysis, canonical correlation analysis, linear programming prob- lem; Problems related to Machine Learning techniques: classi cation methods, resampling methods-di erent cross-validation and bootstrap, linear model selection procedures, regular- ized methods-lasso, elastic net, group lasso, and bridge, dimension reduction techniques, linear programing probleems.

Course Credit: 2

Course Description: This statistical computing course focuses on real-life applications of the topics covered in the courses: time series analysis and econometrics methods. The course will equip students with the tools and techniques to analyze and interpret time series, and economic and nancial data, make forecasts, estimate economic relationships, and contribute to economic research and policy analysis by integrating statistical software R, Stata, or Python. Course Objectives: The course's main objective is to familiarize the students with statistical software and packages (R, Stata, or Python) to apply time series and econometric methods for analyzing data and solving real-life problems. The aim is to prepare students with the skills and knowledge necessary to pursue careers in economics, nance, data analytics, or research institutions where time series analysis and econometrics are essential. Learning Outcomes Upon completion of the course, students are expected to be able to CLO1 comprehensive understanding of time series and econometric models, and the skill to interpret and evaluate results and make informed decisions based on their anal- yses. CLO2 understand how to t various time series and econometric model to real-life data and identify the best models. CLO3 pro ciently use of statistical software such as R, stata to perform di erent kinds of econometric modeling and visualization. CLO4 pro ciently use of statistical software such as R, stata to perform di erent kinds of time series analysis and visualization. CLO5 discuss the use of statistical models related to time series and econometric data frame and solutions to the problems faced by the di erent stakeholders. Contents Exploratory analysis of time series data, tting time series models such as ARMA, ARIMA, etc. Fitting econometric models.

Course Credit: 2

Course Description: This course deals with the implementation of GLMs and survival models to real-life data from diverse areas such as medicine, biological science, engineering, and social science. In addition, this course demonstrates the use of statistical software and packages (e.g., R or Stata) to compute the models using real-life data. Course Objectives: The objectives of the course are to teach students the application of a broader range of statistical models to analyze real-life data from diverse areas. Secondly, to equip students with skills to use statistical software and packages (e.g., R or Stata) to compute the models and discuss the models and results with other researchers and stakeholders. Learning Outcomes Upon completion of the course, students will be able to CLO1 develop a solid understanding of the implementation of GLMS and survival models for their use in practice CLO2 understand how to formulate and t a model for a dataset and interpret the esti- mates of the model parameters CLO3 develop computational skills to use statistical software for tting the models to a dataset CLO4 demonstrate skills to use these models to analyze data from diverse areas and discuss the ndings with researchers from other disciplines CLO5 discuss the use of statistical models for data-driven solutions to the problems faced by the industries and other stakeholders Contents Exploratory analysis of categorical data, tting glm: logistic regression models, binary logistic, multinomial logistic, ordinal logistic, log-linear models; Fitting survival models: AFT, Cox PH models, competing risks models, and frailty models.

Course Credit: 2

Each student must be examined by a committee of selected members at the end of the aca- demic year.

Course Credit: 3

Each student will be required to prepare a project report and present the report in a seminar. The project report is expected to re ect a student's ability to apply his or her knowledge of statistical methods in a nobel research work, which could be applied or theoretical. For the project work, each student will be assigned to a supervisor (a faculty member of ISRT) at the beginning of the academic year. The project report submission and presentation should be made before the nal examination. The 50% weight of the course will be allotted to project work, 10% for supervisor, and the remaining 40% for seminar presentation. The internal members of the examination committee will evaluate the performance in the seminars, and the report will be evaluated by two internal examiners nominated by the examination committee. A supervisor cannot evaluate the project report s/he has supervised.