## Level III Course Units

Semester | Pre Req | Course | Title | Credits | Hours | Type |
---|---|---|---|---|---|---|

I | ST 3003 | Marketing Research | 2 | 30L | o | |

I | ST 3007 | Operational Research | 3 | 45L | o | |

I | ST 3051 | Statistical Inference I | 3 | 45L | x | |

I | ST 1004, ST 2004 | ST 3072 | Applied Regression Analysis | 3 | 45L | x |

I | ST 3074 | Time Series Analysis | 2 | 30L | x | |

I | ST 3075 | Design of Experiments | 2 | 30L | x | |

I | ST 3085 | Computational Statistics | 2 | 15L 30P | x | |

II | ST2008/MS2001 | ST 3012 | Statistical Process Control | 2 | 30L | o |

II | ST 3013 | Essential Mathematics for Statistics | 3 | 45L | x | |

II | ST 3070 | Special Topics | 2 | 15L 30P | o | |

II | ST 3073 | Survey and Sampling | 3 | 45L | x | |

II | ST 3077 | Medical Statistics | 3 | 45L | o | |

II | ST 3082 | Statistical Learning I | 2 | 60P | x | |

II | ST 3083 | Multivariate Data analysis | 3 | 45L | x | |

II | ST 3051 | ST 3084 | Statistical Inference II | 2 | 30L | x |

**Note:** Students may take a maximum of 33 credits. Abbreviations : x – core courses, o – electives, L – lectures, P – practicals

## Level IV Course Units

Semester | Pre Req | Course | Title | Credits | Hours | Type |
---|---|---|---|---|---|---|

I | ST 4011 | Econometrics | 2 | 30L | o | |

I | ST 4031 | Stochastic Processes and Application | 3 | 45L | x | |

I | ST 4051 | Scientific Writing | 1 | 30P | x | |

I | ST 4052 | Statistical Learning II | 2 | 60P | x | |

I | ST 4055 | Generalized Linear Models | 3 | 30L 30P | x | |

II | ST 4012 | Special Topics for ST | 2 | 30L | o | |

II | ST 4050 | Individual Project ST | 8 | 240P | x | |

II | ST 3051, ST 3084 | ST 4053 | Bayesian Statistics | 2 | 30L | x |

II | ST 4054 | Linear Models | 3 | 45L | x | |

II | EC 4004 | Industrial Training | 0 | 90P | o |

**Note:** Abbreviations : x – core courses, o – electives, L – lectures, P – practicals

**ST 3051 – Statistical Inference I – [3credits (45L), For ST (core), ST+CS (core)]**

**Intended Learning Outcomes:**

Upon successful completion of the course, students should be able to recognize the underlying theory behind statistical estimation, apply the necessary techniques to find estimates of population parameters and appraise the properties of estimators.

**Course Content:** Generating moments using characteristic function; Sampling from Normal population: sampling distributions of sample mean and sample variance (s2), independence of sample mean and s2; Properties of estimators: Mean-squared error, Unbiasedness, Consistency, Sufficiency, Completeness, Efficiency; Factorization criterion; Variance Reduction: Cramer-Rao Lower Bound, Rao-Blackwell Theorem, Lehmann-Scheffe’ Theorem; Methods of Estimation: Method of moments, Maximum Likelihood and Its Properties, Least Squares; Interval Estimation: Pivotal Method, General Method.

**Method of Delivery:** Interactive classroom sessions

**Evaluation Criteria:** End-of-semester examination (70%) and assignments (30%)

**Suggested Readings:** Introduction to Mathematical Statistics (Hogg and Craig), Statistical Theory (Lindgren), Introduction to the Theory of Statistics, 3rd Edition (Mood , Graybill and Boes)

**ST 3072 – Applied Regression Analysis – [3credits (45L), For ST (core), ST+CS (core)]**

**Prerequisites:** ST1004 and ST2004

**Learning Outcomes:** At the completion of the course, the students should be able to formulate a suitable regression model to describe a relationship between a response variable and one or more explanatory variables. The students will also be able to apply appropriate diagnostics to evaluate the model and interpret the model to describe the problem.

**Course Contents:** Simple Linear Regression: introduction, correlation, uses of Regression, simple linear Regression model, parameter estimation, inferences about the model, prediction, coefficient of determination; Model Adequacy: residuals, outliers, lack of fit, transformations; Multiple Linear Regression: Multiple Linear Regression model, parameter estimation, inferences about the model, prediction, model adequacy, variable selection methods, use of categorical variables as predictors, analysis of co-linearity; Transformation of Variables; Polynomial regression; weighted least square

**Method of Delivery:** Lectures

**Method of Evaluation:** Based on end of semester examination (70-80%) + Continuous Assessment (30-20%)

**Suggested Readings:** Applied Regression Analysis, Third edition, Wiley (Draper, N.R. and Smith, H.), Applied Regression Analysis and Other Multivariable Methods. Third Edition. Duxbury Press (Kleinbaum, Kupper, Muller, and Nizam.), Regression Analysis by Example, Third Edition, Wiley (Chatterjee, S. and Hadi, A. L.), Introduction to Linear Regression Analysis, Wiley (Montgomery, D. C. and Peck E. A.)

**ST 3085 – Computational Statistics – [2 credits (30L), For ST (core), IS(core) ST+CS (optional)]**

**Learning Outcomes:** After a successful completion, students should be able to generate random numbers; simulate data; apply bootstrap methods to analyze data.

**Course Content:** Introduction to Random numbers: pseudo random numbers, properties of random numbers, testing for basic properties, software for random number generation; Introduction to Simulation: simulation of random variables, Monte Carlo simulation methods, simulation of inventory models, simulation of queuing models; Data Re-sampling: Introduction to Bootstrap, Bootstrap estimation of Variance, Bootstrap Confidence Intervals, Introduction to EM algorithm.

**Method of Delivery:** Lectures and lab sessions

**Evaluation Criteria:** End-of –semester examination (70%) and continuous assessments (30%)

**Suggested Readings:** Computational Statistics (Givens, G. H. and Hoeting, J. A.), Elements of Computational Statistics (Gentle, J. E), An introduction to the bootstrap (Efron and Tibshirani).

**ST 3074 – Time Series Analysis– [2credits (30L), For ST (core), ST+CS (optional)]**

**Learning Outcomes:** Upon the successful completion students should be able to model and forecast univariate time series.

Course Content: Introduction: definition, types of time series, components of time series, time plot, time series decomposition, transformation, differencing, autocorrelation; Stationarity: stationary & non-stationary time series, tests for stationarity; Modelling time series: time series models, model identification, parameter estimation, diagnostic checks, forecasting.

**Method of Delivery:** Lectures and Practicals

**Method of Evaluation:** End-of-semester examination (80%) and In-class Assignments (20%)

**Suggested Readings:** Forecasting Methods and Applications (Makridakis, S. Weelwright, S. C. and Hyndman, R. J.), The analysis of Time Series: An Introduction (Chatfield, C), Forecasting and Control (Box, G. E. P., Jenkins, G. M. and Reinsell)

**ST 3075 – Design of Experiments – [2credits (30L), For ST (core)]**

**Learning Objectives and Outcomes:** At the end of the course student are expected to employ basic planning and designing skills to propose suitable experimental designs, analyze data and interpret results to answer specific questions in comparative experiments.

**Course Content:** Principles of planning and designing comparative experiments; Review of ANOVA and related topics; Basic designs: completely randomized design (CRD), randomized complete block design (RCBD), Latin squares/multiple Latin squares, treatment contrasts and mean comparisons; Factorial experiments (2k and others); confounding and partial confounding in 2k experiments; split-plot designs; analysis of covariance.

**Method of Delivery:** Lectures

**Method of Evaluation:** End-of-semester examination and Assignments

**Suggested Readings:** Design and analysis of experiments (Montgomery, D. C.), Design of Experiments: Statistical principles of research design and analysis (Kuehl, R.O.), Statistics for experiments: An introduction to design, data analysis and model building (Box, Hunter, and Hunter).

**ST 3083 – Multivariate Data Analysis– [3credits (45L), For ST (core), ST+CS (core), IS (elective)]**

**Learning Outcomes:** After a successful completion, students should be able to make decisions based on multivariate hypothesis tests; carryout dimension reduction methods; clustering data and discriminate new observations to pre-defined clusters

**Course Content:** Review of matrix algebra; Mean and variance-covariance of a random vector; correlation matrix; Properties of multivariate normal distribution and applications; Checking for multivariate normality; Hypothesis testing using multivariate tests; MANOVA ; Principal component analysis; Factor analysis; Discriminant analysis; Cluster analysis.

**Method of Delivery:** Lectures

**Method of Evaluation:** End-of-semester examination and Assignments

**Suggested Reading:** Applied multivariate statistical analysis (Johnson and Wichern), Multivariate statistical methods (Morrison), Applied multivariate methods for data analysts (Johnson).

**ST 3084 – Statistical Inference – II– [2credits (30L), For ST (core), ST+CS (core)]**

**Pre-requisites:** ST 3051

**Intended Learning Outcomes:** Upon successful completion of the course, students should be able to recognize the underlying general theory behind testing statistical hypotheses and apply the necessary techniques to real life situations.

**Course Content:** Parametric Inference: Introduction to Hypothesis Testing, Errors, Power, Neymann-Pearson Lemma, Most Powerful Tests, Uniformly Most Powerful Tests, Likelihood Ratio Tests, Sequential Tests, Sequential Probability Ratio Test (SPRT), Wald’s Identity, Average Sample Number (ASN); Distribution-free Inference: Tests of Randomness, Run Tests, One sample Location Tests for Median, Sign Test; Asymptotic Relative Efficiency (ARE); Two sample Location problem.

**Method of Delivery:** Interactive class room sessions

**Evaluation Criteria:** End-of-semester examination (70%) and assignments (30%)

**Suggested Readings:** Introduction to the Theory of Statistics, 3rd Edition (Mood , Graybill and Boes), Statistical Theory (Lindgren), Introduction to Mathematical Statistics (Hogg and Craig)

**ST 3073 – Survey and Sampling – [3credits (45L), For ST (core)]**

**Learning Objectives and Outcomes:** After the completion of the course, the students should be able to recognize the building blocks and the theory of random sampling design a survey and be able to estimate parameters based on the design of the study.

**Course Content:** Fundamentals of probability sampling and estimation; Simple Random Sampling: theory involved in estimation procedures, sampling weights, estimating population mean, variance, total & proportion, estimating a ratio & its variance, estimation using Ratio and Regression methods and their properties, Sample size determination; Stratified Random Sampling: proportional and optimal cost allocation to strata, estimating population mean, variance, total & proportion, overview of advanced topics in stratified random sampling, Estimating a ratio & its variance, regression estimators, sample size determination, post-stratification, quota sampling; Cluster Sampling: overview of cluster sampling, clustering with equal and unequal probabilities, sample size determination, design effect and intra-cluster correlation; Multi-stage sampling: Complex surveys and related problems, sources of errors in surveys.

**Method of Delivery:** Interactive class room sessions

**Method of Evaluation:** End-of-semester examination (70%) and Assignments (30%)

**Suggested Readings:** Design and Analysis (Sharon L. Lohr), Sampling Techniques (William G. Cochran), Elementary Sampling Theory (Vic Barnet), Survey Sampling (Leslie Kish)

**ST 3077 – Medical Statistics –[3credits (45L), For ST (elective)]**

**Course Contents:** Introduction; Epidemiology: basic designs for epidemiological studies, relative risk and odds ratio, confounding and interaction; Analysis of data from cohort and case control studies; Matched case control studies; Logistic regression; Clinical trials: introduction, protocols for clinical trials, cross-over designs, allocation to treatment, sample size determination, Phase I and Phase II studies; Survival Analysis: analysis of survival data, the survival and hazard functions; Non-parametric procedures: Kaplan-Meier estimate of survivor functions, log-rank test for comparing two survival times; Parametric modeling: proportional hazards model, Cox’s proportional hazards model.

Intended Learning Outcomes: At the successful completion student should be able to define, compute and interpret statistics; identify and apply statistical models in epidemiology, clinical trials, and survival studies in order to analyze data from medical studies.

**Method of Delivery:** Interactive class room sessions

**Method of Evaluation:** Based on end of semester examination (70% or 80%) + Continuous Assessment (30% or 20%)

**Suggested Readings:** Statistical methods in medical research (Armitage, P.), Case-control studies

**ST 3082 – Statistical Learning I – [2credit (60P), For ST (core), ST+CS (core), IS (core)]**

**Indented learning outcomes:** Upon completion of this course, student should be able to explore complex data sets, select appropriate statistical techniques to solve problems involved and justify their choice. The students should be able to implement these techniques using an appropriate programming language, evaluate the results and explain the results to non statisticians using non statistical terms.

**Course Contents:** Introduction to statistical learning; Advanced regression model: understanding models, variable selection, validation and cross validation, Shrinkage method and ridge regression, Lasso, principal component regression and partial least squares; Resembling method: cross validation, bootstrap; Classification: understanding classification problems using logistic regression, multivariate logistic regression, and discriminate analysis.

**Method of Delivery:** Interactive lab sessions and assignments

**Evaluation Criteria:** Assignments

**Suggested Readings:** An Introduction to Statistical Learning by James, Witten, Hastie, and Tibshirani

**ST 3013 – Essential Mathematics for Statistics – [3 credit (45L), For ST (core), ST+CS (core), IS (core), 4G (core)]**

**Learning Outcomes:** After a successful completion, students should be able to apply basic mathematical tools in solving theoretical and practical problems in Statistics.

**Course Content:** Linear algebra: Linear dependence, rank and the solution of homogeneous equations, characteristic polynomials, eigenvalues , eigenvectors, spectral theorem for symmetric matrices, idempotent matrices and properties, orthogonal projections, trace of a matrix and properties, positive definite/semi definite matrices, quadratic forms, differential calculus in matrix notation, direct product (kronecker)of any two matrices, generalized inverse /conditional inverse ; Calculus: Concepts of functions, limits and continuity, L’Hopital’s rule, the fundamental theorem of calculus, approximation of definite integrals, Improper integrals; Series and Sequences: sequences and their convergence, series and convergence of series, power series and their convergence of radius, Taylor series and their application; Several variable calculus: functions of several variables, continuity, differentiability, derivatives, multiple integrals, change of variables

**Method of Delivery:** Lectures

**Method of Evaluation:** End-of-semester examination

**Suggested Reading:** Matrices with applications in Statistics (Graybill, F. A.), Real Infinite Series (D. Bonar and M. Khoury), Introduction to Calculus and Analysis, Volume 1 (Richard Courant and Fritz John), Calculus of several variables ( Serge Lang)

**ST 4051 – Literature Review – [1credit (30P), For ST (core), ST+CS (core), IS (core)]**

**Learning Outcomes:** Upon completion of this course, student should be able to search, identify, read, and analyze research articles which are relevant to their research activities; Write a quality scientific literature review for a selected research problem.

**Course content:** Read and discuss text/papers for a general sense of what research is/are about, how one thinks when doing research, and what the major research activities are; Identify research articles from different areas of statistics/computer science, involving different methodologies of research, and abstract them; Select an area related to statistics, which is of particular interest to students, write a professional quality literature review for a problem of your choice.

**Method of Delivery:** Interactive class room sessions and assignments

**Evaluation Criteria:** Assignments

**ST 4055 – Generalized Linear Models – [3credits (30L), For ST (Core), ST+CS (elective)]**

**Intended Learning Outcomes:** At the completion of the course, the students should be able to identify and apply a suitable generalized linear model for a given dataset. Student should also be able to apply appropriate diagnostics to evaluate the model.

**Course Contents:** Introduction to Statistical modeling; Exponential family and GLMs: estimation, inference; Logistic regression: binary logistic model, link function, over dispersion and bio-assay, multinomial logistic model, ordinal logistic model; Log-linear models: contingency tables, link function; comparison of logistic and log-linear models; Gamma models; Model Adequacy: residuals, outliers, lack of fit.

**Method of Delivery:** Lectures

**Evaluation Criteria:** Based on end of semester examination (70%) + In-class Assignments (30%)

**Suggested Readings:** Categorical Data Analysis (Alan Agresti), Modelling Binary Data (D. Collett), Generalized Linear Models (McCullah and Nelder), Statistical Modelling in GLIM (Aitkin, M., Anderson, D., Francis, B., and Hinde, J. )

**ST 4031 – Stochastic Process and Application – [3credit (45L), For ST (core), ST+CS (core), IS (core)]**

**Intended Learning Outcome:** Upon successful completion of this course, students should be able to recognize the properties of basic stochastic processes and apply the knowledge of probability theory and stochastic processes to analyze problems in practice.

**Course Content:** Generating function; Basics of Brownian motion; Poisson process; Random walks; Discrete parameter Markov Chains; Continuous parameter Markov Chains; Branching process; Birth and Death processes; Queuing processes.

Method of Delivery: Interactive class room sessions

**Evaluation Criteria:** End-of-semester examination (70%) and assignments (30%)

Suggested Reading The Elements of Stochastic Processes(Bailey), An Introduction to Probability Theory and Applications (Feller), Stochastic Processes(Cox & Miller), Probability and Statistics with Reliability Queues and Computer Science Applications (Kishor S. Trivedi)

**ST 4052 – Statistical Learning II – [2credit (60P), For ST (core) , ST+CS (core), IS (core)]**

**Indented learning outcomes:** Upon completion of this course, student should be able to explore complex data sets, select the relevant statistical techniques discussed to solve problems involved and justify their choice. The students should be able to implement these techniques using an appropriate programming language, evaluate the results and explain the results to non statisticians using non statistical terms.

**Course Contents:** Moving beyond linearity: polynomial regression, regression splines, smoothing splines; Tree-based methods: the basics of decision tree, bagging, random forest, boosting; Support Vector machines; Unsupervised learning: dimension reduction techniques, clustering

**Method of Delivery:** Interactive lab sessions and assignments

**Evaluation criteria:** Assignments

**Suggested reading:** An Introduction to Statistical Learning by James, Witten, Hastie, and Tibshirani

**ST 4053 – Bayesian Statistics – [2credits (30L), For ST (core)]**

**Pre-requisites:** ST 3051, ST 3084

**Learning Objectives and Outcomes:** Upon completion of this course students should be able to apply basic concepts in Bayesian approach to statistical thinking and use Bayesian techniques to analyze data related to the practical applications.

**Course Contents:** Basics: Bayes theorem, difference between classical statistics and Bayesian statistics, prior distributions, posterior distributions, hypothesis testing, credible sets; Single Parameter Models: normal and binomial distributions; Multi Parameter Models: multinomial model, hierarchical models, linear regression, generalized linear models, large sample theory

**Method of Delivery:** Lectures

**Method of evaluation:** End-of-semester examination (70%) and Assignments (30%)

**Suggested Readings:** Bayesian Data Analysis (Andrew Gelman, John B. Carlin, Hal S. stern and Donald B. Rubin)

**ST 4054 – Linear Models – [3credits (45L), For ST (core)]**

**Intended Learning Outcomes:** Upon successful completion of the course, students should be able to recognize the fundamentals of the general linear model, distinguish between different linear models found in real life situations and appraise the optimal estimation and inference related to different linear models.

**Course Content:** Elementary linear and matrix algebra: idempotent matrices, trace of matrices, generalized and conditional inverses; Solutions of linear equations; Derivatives of quadratic forms; Expectation of random matrices; Multivariate normal distribution and its properties; Distribution of quadratic forms; General linear model: optimal estimation and hypothesis testing, applications to regression model, continued application of optimal inference, design models, estimability, solving normal equations, components of variance models and mixed models

**Method of Delivery:** Interactive class room sessions

**Evaluation Criteria:** End-of-semester examination (70%) and assignments (30%)

**Suggested Readings:** Theory and applications of the linear model (Graybill, F. A.), Matrices with applications in Statistics (Graybill, F. A.),Plane answers to complex questions ( Ronald Christensen)