### Level – 3M

#### Course units effective from academic year 2016/2017 to date

 Course Code STA301M3 Course Title Advanced Design of Experiments Credit Value 03 Prerequisite    Prerequisite STA203G3 Hourly Breakdown Theory Practical IndependentLearning 45 – 105 Objective: Provide an introduction to the  block  and factorial  experimental designsIntroduce and explain the design aspects of the experiments Intended Learning Outcomes: Explain the mathematical models and issues such as interaction, confounding etc.Construct  factorial experiments confounded with blocksDesign fractional factorial experimentsAnalyze experimental data of  incomplete block designs Course Contents: Factorial Designs: 2k Factorial Designs, 3kFactorial Designs, Yates’ Algorithm, Blocking, Confounding, Partial Confounding, Fractional Factorial Designs, Design Resolution, Blocking Fractional Factorials, Alias Structure.Block Designs: Randomized Complete Block Design, Latin Square Design, Balanced Incomplete Block Design, Graeco- Latin Square Design, Partially Balanced Incomplete Block Design, Youden Square Design. Teaching Methods: Lectures and  Tutorial discussions Assessment/ Evaluation Details: In-course Assessments               30%End-of-course Examination       70% Recommended Readings: Douglas C. Montgomery., Design and Analysis of Experiments, Wiley Series, 2013.H.R. Lindman., Analysis of Variance in Experimental Design, Springer Series, 1992.R. A. Fisher., The Design of Experiments, Oliver and Boyd, 1960.G. W. Cobb., Design and Analysis of Experiments, Springer Series, 1998.

STA302M3: Medical Statistics

 Course Code STA302M3 Course Title Medical Statistics Academic Credits 03 Hourly Breakdown Theory Practical IndependentLearning 45 – 105 Objective: Introduce the statistical methods used in medical science Intended Learning Outcomes: Discuss  common terms used in epidemiologyDiscuss direct and indirect methods of adjustment of overall ratesCompare the disease occurrence between two groupsEvaluate the common odds ratio with confidence intervalDiscuss observational and experimental studies in medical fieldCompare the analytical studies in medical fieldTest the possible effects in crossover trialExpress the relationship among the survival function, distribution function, hazard function and cumulative hazard functionEstimate survival function using parametric and non-parametric methods Illustrate two-sample comparison for survival data using common statistical proceduresApply Cox proportional hazard model to real life data Course Contents: Epidemiology: definition of  epidemiology, measuring disease frequency: population at risk, incidence, prevalence, case fatality, birth rate, death rate, life expectancy, direct and indirect standardized rate, comparing disease occurrence: absolute and relative comparison, common odds ratio: Cochran Mantel Haenszel and logit method, confidence interval for common odds ratio, Cochran Mantel Haenszel testTypes of studies: observational studies: descriptive and  analytical studies, ecological, cross-sectional, case-control and cohort studies, experimental studies: clinical trial, parallel group design, in-series design and crossover designSurvival Analysis: censoring, survival function, hazard function, cumulative hazard function, mean and median survival time, mean residual life time, estimation of survival function: parametric and non-parametric method: Kaplan-Meier estimator, life table, cumulative hazard estimator, two sample comparison: log-rank test, maximum likelihood test and likelihood ratio test, Cox proportional hazard model Teaching Methods: Lectures and Tutorial discussions Assessment/ Evaluation Details: In-course assessments             30% End of course Examination     70% Recommended Readings: David W. H., Stanley, L. and Susanne M., Applied Survival Analysis: Regression Modeling of Time to Event Data, John Wiley and Sons, New Jersey, 2008.Bonita, R.,Beaglehole, R. and Kjellstrom, T., Basic Epidemiology, 2nd edition, World Health Organization, 2006.Kleinbaum, D.G., Survival Analysis: A Self-Learning Text, Springer, New York, 1996.

STA303M3: Categorical Data Analysis

 Course Code STA303M3 Course Title Categorical Data Analysis Academic Credits 03 Hourly Breakdown Theory Practical IndependentLearning 45 – 105 Objective:Provide knowledge for analyzing categorical data. Intended Learning Outcomes: Discuss major types of categorical data and their probability distributionsApply appropriate descriptive and inferential statistical methods for contingency tablesBuild appropriate statistical models for different types of categorical response dataAnalyze repeated/longitudinal categorical response data Course Contents: Introduction:Categorical response data, Probability distributions for categorical data: Bernoulli, binomial, multinomial, and Poisson,Likelihood function and Maximum likelihood estimate, Likelihood‐based inference methods: Wald test, score test.Contingency tables:Two-way contingency tables; Table structure, comparing proportions, relative risk, odds ratio, Pearson’s Chi-square test, Likelihood ratio test, testing independence for ordinal data, Fisher’s exact test for small samples.Three-way Contingency tables; Conditional versus marginal tables, Simpson’s paradox, Conditional versus marginal odds ratios, Conditional versus marginal independence, Cochran-Mantel-Haenszel (CMH) test Homogeneous association for   tables.Generalized Linear Model (GLM):Components of generalized linear models, GLMs for binary and count data; Logistic regression and Log-linear model, Statistical inference for GLM, Comparing models, Model selection, Model diagnostics, Logit models, Probit Models, Analysis of repeated responses. Teaching Methods: Lectures  and tutorial discussions Assessment/ Evaluation Details: In-course assessments              30%End of course Examination     70% Recommended Readings: Agresti. A, Categorical Data Analysis, 3rd  Edition. New York: Wiley, 2012.McCullagh. P, and Nelder. J. A, Generalized Linear Models, 2nd Edition, London: Chapman and Hall, 1989.Powers. A. D, and Y. Xie., Statistical Methods for Categorical Data Analysis, San Diego, CA: Academic Press, 2000.

STA304M3: Computational Statistics

 Course Code STA304M3 CourseTitle Computational Statistics Credit Value 03 Hourly Breakdown Theory Practical Independent Learning 15 60 75 Objectives: Provide an introduction to the  computational statisticsIntroduce some software for the statistical computing Intended Learning Outcomes: Formulate simple functions for data managementDevelop  algorithms for simulation of random numbersApply Monte- Carlo simulation techniques to  real world problemsApply Bootstrap methods to real world problemsDevelop the ability to use some statistical software in a real world situation. Course Contents: Introduction: Make use of a statistical software to write simple functions for data management and analysisSimulation of random numbers: Box-Muller Algorithm, Inverse Transformation Method, Acceptance-Rejection Method, Polar Algorithm, CompositionMonte- Carlo methods: Monte-Carlo integration, Markov chain Monte Carlo methods,  Metropolis-Hastings algorithms,  the Gibbs samplerBootstrap methods: Bootstrap re-sampling techniques,  Bootstrap confidence intervals, Bootstrap estimate of bias Teaching Methods: Lectures,  Laboratory practical, group assignments and e-resources Assessment/ Evaluation Details: In-course Assessments               30%End-of-course Practical Examination       70% Recommended Readings: Wendy L. Martinez, Angel R. Martinez, Computational Statistics handbook with MATLAB, Chapman and Hall/CRC, 2015.Venables, W.N., Ripley, B.D., Modern Applied Statistics with S, Springer Series, 1999.MoonJung Cho, Wendy L. Martinez., Statistics in MATLAB: A Primer, Chapman and Hall/CRC, 2014.

STA305M3: Time Series Analysis

STA306M3: Multivariate Analysis I

 Course Code STA306M3 Course Title Multivariate Analysis I Academic Credits 03 Hourly Breakdown Theory Practical IndepInde  Independent Learning 45 – 105 Objective: Introduce multivariate techniques and their applications to real world problems Intended Learning Outcomes: Distinguish univariate and multivariate data Find mean vector, covariance matrix and correlation matrix for a multivariate dataDetermine the distribution of linear combination of random variablesDiscuss the use of Wishart distribution in multivariate dataDiscuss the properties of multivariate normal and Wishart distributionsApply Hotelling T2 statistics for testing the plausible value for mean vectorCompare several covariance matricesApply statistical tests to multivariate normal distributionsConstruct confidence intervals for mean vector and treatment effects Syllabus Outline Course Contents: Introduction :Multivariate Data, Multivariate marginal and conditional distributions, mean vector, variance-covariance and correlation matrices, properties of covariance and correlation matrices, linear combination of random variablesMultivariate distribution : Multivariate Normal distribution; probability density of multivariate Normal distribution and its properties, transforming multivariate observations, multivariate likelihood estimation of mean vector and covariance matrix, Wishart distribution; Probability density of Wishart distribution and its properties, Sampling distribution of sample mean vector and sample covariance matrixInference about mean vector :Hotelling T2 distribution, Hotelling T2 test for plausible value for mean vector, confidence region, Comparisons of component means: Simultaneous and Bonferroniconfidence intervals, large sample inference about population mean vector, profile analysisComparison of several multivariate means : Comparing mean vectors from two population, simultaneous and Bonferroni confidence intervals, Large sample inference for comparing mean vector, profile analysis, Box-M test for comparing several covariance matrices, Paired comparisons, One way MANOVA, Two way MANOVA, Simultaneous and Bonferroni confidence intervals for treatment effects Teaching Methods: Lectures,  demonstration and Tutorial discussions Assessment/ Evaluation Details: In-course assessments             30%End of course Examination     70% Recommended Readings: Chatfield, C., and Collins, A. J., Introduction to multivariate analysis, New York: Chapman and Hall, 1980.Johnson, R. A., and Wichern, D. W., Applied multivariate statistical analysis, Englewood Cliffs, 6th Edition, N.J: Prentice Hall, 2006.Everitt, B. S. and Hothorn T., An Introduction to Applied Multivariate Analysis with R, Springer, (2011).

### Level – 4M

#### Course units effective from academic year 2016/2017 to date

STA401M4: Measure Theory

 Course Code STA401 M4 Course Title Measure Theory Credit Value 04 Prerequisites PMM202G2 and PMM203G3 Hourly Breakdown Theory Practical Independent Learning 60 — 140 Objectives: Introduce the fundamental concepts of Lebesgue measure spaces and abstract measure spaces Develop clear ideas on the concept of Lebesgue measurable functions, integrals, and their convergence propertiesDiscussthe fundamental connection between differentiation, and integration Intended Learning Outcomes: Construct Lebesgue measures on the real lineDefine abstract measure spaceIllustrate the properties of abstract measure spaceDiscuss the properties of measurable functions and the convergence of sequence of measurable functionsExplain the simple function approximation of measurable functionsFormulate integrals in a measure spaceDiscuss the convergence of integralsExtend the measures from algebras/semialgebra to σ-algebrasFormulateproduct measuresProve Fubini’s theorem, and Tonelli’s theoremDiscuss the fundamental connection between differentiation, and integration Course Contents: Measure Spaces:Preliminaries:Algebra and σ-algebras of sets,Borel sets; Lebesgue measure: Outer measure, Measurable sets, and Lebesgue measure,Properties,Example of a non-measurable set, Borel measures; General measure: Definition of measure, Measure space, Complete measure space, Examples, Properties.Measurable Functions:  Basic properties of measurable functions, Examples, Borel measurable functions, Approximation Theorem; Littlewoods’s three principles: Egoroff’s theorem.Integration:Integral of nonnegative functions, Integrability of a nonnegative function, Fatou’s Lemma, Monotone convergence theorem, Lebesgue Convergence Theorem, Generalized Convergence Theorem.Extension of Measure:Measure on an algebra, Extension of measures from algebras to σ-algebras, Carathéodory’s theorem, and Lebesgue-Stieltjes integral.Product Measure:Measurable rectangle, Semialgebra, Construction of product measures, Fubini’s theorem, and Tonelli’s theoremDifferentiation and Integration:Differentiation of monotone functions: Vitali’s lemma, Functions of bounded variations; Differentiation of an integral: Indefinite integral, and Absolutely continuous functions. Teaching Methods: Lectures, Tutorials, Handouts, Problem solving, Use of e-resources Assessment/ Evaluation Details: In-course Assessments         30% End-of-course Examination 70% Recommended Readings: Halsey Royden, Patrick Fitzpatrick, Real Analysis,4th Edition, 2010.Walter Rudin, Real and Complex Analysis, 3rd Edition, 1986. G De Barra, Measure theory and Integration, 2nd Edition, 2003.Gerald, B. Folland, Real Analysis: Modern Techniques and Their Applications, 2nd Edition, 2007.

 Course Code STA402M2 Course Title Advanced Statistical Computing Academic Credits 02 Hourly Breakdown Theory Practical Independent Learning – 60 Hours 40 Hours Objective: Introduce the Statistical concepts and principles to perform numerical computation using statistical software Intended Learning Outcomes: Utilize build-in functions to analyze categorical data setsAnalyse the survival data by applying build-in functionsDevelop time series models using statistical softwareList summary statistics for given multivariate data setsExamine the effects of factors by applying build- in functionsExplore standard statistical methods using statistical softwareWrite computer programms to accomplish a task Syllabus Outline Contents: Analysis of large data sets: Build-in functions for categorical data, survival data, time series data and multivariate data.Analysis of experimental data sets: Analysis of variance (ANOVA), multivariate hypothesis tests, Multivariate Analysis of variance (MANOVA)Simple function: writing simple functions to perform specific tasks. Teaching Methods: Laboratory practical Assessment/ Evaluation Details: In-course assessments (practical)          30%End of course Examination (practical)  70% Recommended Readings: Lafaye de Micheaux, Pierre and Drouilhet, Rémy and Liquet, Benoit, The R software: Fundamentals of programming and statistical analysis, Springer, 2013. Michael, J. Crawley ,The R Book, Second Edition, John Wiley and Sons, Ltd, 2013.Dirk, F. Moore, Applied Survival Analysis Using R, Springer, 2016.Daniel Zelterman, Applied Multivariate Statistics with R, Springer, 2015.Robert H. Shumway and David S. Stoffer, Time Series Analysis and Its Application With R Examples, Springer, 2011.

STA403M3: Markov Processes for Stochastic Modelling

 Course Code STA403M3 Course Title Markov Processes for Stochastic Modelling Academic Credits 03 Prerequisite STA302G3 Hourly Breakdown Theory Practical Independent Learning 45Hours _ 105 Hours Objectives: Impart sound understanding on the Markov processes and their properties Introduce the basic concept and modelling methods on birth and death processesProvide rigorous knowledge in queueing theory and applications Intended Learning Outcomes: Recall basic characteristics of Markov processesDiscuss important properties of Markov chainEvaluate the first passage and absorption probabilitiesFind stationary distribution of a Markov chainIllustrate the canonical form of a Markov chainModel therelevant birth and death processes for randomly varying dynamic systemsApply Chapman-Kolmogorov equation to formulate the forward differential equationsConstruct probability distribution of random processes Explain the probability generating function for stochastic models Find average waiting time and queue length of the systemsDetermine steady state distribution of a queueing system Syllabus Outline Contents: Markov processes in discrete parameter space: Basic properties of Markov chain,Transition probability matrix, Classification of states (recurrent and transient classes), Periodicity of a class, Irreducible Markov chains, Ergodic Markov chains,First passage and recurrent times, Probabilities of absorption of transient states in one of the recurrent classes, Expected value and standard deviation of the number of transitions till absorption, Stationary distributions, Canonical form, The fundamental matrix. Random walk with absorbing and reflecting barriers.Markov processes in continuous parameter space:Markov pure jump process, Chapman-Kolmogorov equation, Birth and death process, pure birth process, pure death process, Forward and backward Kolmogorov differential equations, transition rate matrix, Analysis of random process using probability generating function, expected value and variance, probability extinction.Queueing processes:Arrival and service processes, single and multiple server queueing systems, Steady state distribution, Traffic intensity, mean of waiting time, Network of queues, Martingale, Stochastic differential equations. Teaching Methods: Lectures, Tutorials, Handouts, Problem solving, Use e-resources Assessment/ Evaluation Details: In-course Assessments:             30%  End-of-course Examination:     70% Recommended Readings: Parzen, E.,StochasticProcesses. SIAM Edition; Society for Industrial and Applied Mathematics Philadelphia, 1999. Sheldon M. Ross,Introduction to Probability Models, 10th ed. Academic Press Elsevier, 2013. Jones, P.W, and Smith, P., Stochastic Processes An Introduction, 1st Edition, ARNOLD A member of the Hodder Headline Group London, Co-published in the USA Oxford University Press Inc, New York, 2001.

STA404M3: Generalized Linear Models for Familial Longitudinal Data

 Course Code STA404M3 Course Title Generalized Linear Models for Familial Longitudinal Data Academic Credits 03 Prerequisite Hourly Breakdown Theory Practical Independent Learning 45 Hours 105 Hours Objective:Provide knowledge in fitting models to familial longitudinal data and apply these models to real life problems. Intended Learning Outcomes: Distinguish familial and longitudinal modelsFormulate marginal and conditional models for the analysis of familial longitudinal dataCompare different types of parameter estimation techniquesApply standard correlation structures for familial longitudinal dataBuild appropriate statistical models for count/binary familial longitudinal data Syllabus Outline Contents: Overview of Linear fixed modelsEstimation of parameters: Method of moments, Ordinary Least Squares method (OLS),  Generalized Least square method (GLS), OLS Vs GLS estimation performance; Estimation under stationary general autocorrelation structure: A class of autocorrelationsFamilial models for count dataPoisson mixed models and basic properties; Estimation for single random effect based parametric mixed models: Exact likelihood estimation Method of moments, Generalized Estimating Equation (GEE) approach , Generalized Quasi-likelihood (GQL) ApproachFamilial models for binary dataBinary mixed models and basic properties: Computational formulas for binary moments; Estimation for single random effect based parametric mixed models: Method of moments,  Generalized Quasi-likelihood approach, Maximum likelihood estimation (MLE)Longitudinal models for count dataMarginal model; Marginal model based estimation of regression effects; Correlation models for stationary count data: Poisson AR(1) model,  Poisson MA(1) model, Poisson Equicorrelation (EQC) model; Inferences for stationary correlation models; Nonstaionary correlation modelsLongitudinal models for binary dataMarginal model; Marginal model based estimation of regression effects; Some selected correlation models for longitudinal binary data; Low-order autocorrelation models for stationary binary data: Binary AR(1) model,  Binary MA(1) model, Binary EQC  model; Inferences in Non-stationary correlation models for repeated binary data Teaching Methods: Lecture demonstration, and tutorial discussions Assessment/ Evaluation Details: In-course assessments              30%End of course Examination     70% Recommended Readings: Diggle, P.,Heagerty, K.Y.Liang, K.Y. and Zeger, S. L, Analysis of Longitudinal Data, 2nd  Edition, Oxford University Press, Oxford, 2002.Brajendra, C. Sutradhar, Dynamic Mixed Models for Familial Longitudinal Data, Springer, 2011. McCullagh, P and Nelder, A. J, Generalized Linear Models, Chapman and Hall, 1989.

 Course Code STA405M3 Course Title Advanced Statistical  Theory Academic Credits 03 Prerequisite Hourly Breakdown Theory Practical Independent  Learning 45 Hours – 105 Hours Objective:Introduce concept of advanced statistical theory Intended Learning Outcomes: Recall sufficient statistics, minimal sufficient statistics, complete sufficient statisticsIdentify the exponential families of distributionProve Basu’s theorem and use it for showing independence of statisticsObtain point estimator using various estimation techniquesProve Cramer-Rao  inequality, Rao- Blackwell, Lehmann-Sceffé theoremsFind minimum variance of an unbiased estimator using Cramer-Rao  inequalityObtain the minimum variance unbiased estimator for various probability distributionAnalyze point estimators in terms of consistency, asymptotic normality and efficiency propertiesDetermine interval estimatorsEvaluate the efficiency of the interval estimatorsApply statistical methods for hypothesis testingProve Neyman-Pearson lemma Course Contents: Data Reduction: Scale and location families, sufficiency, factorization theorem, minimal sufficiency, ancillary statistics, complete statistics, Basu’s theorem, exponential families; one parameter case,  parameter casePoint Estimation: Method of moments, maximum likelihood, properties of maximum likelihood estimator, Bayesian point estimation; prior and posterior distributions, bias, variance, mean square error, minimum variance unbiased estimator, Fisher information, Cramer-Rao lower bound, the Rao-Blackwell theorem, the Lehmann-Sceffé theorem, large sample theory; consistency, asymptotic normality and related properties, asymptotic efficiency and optimalityInterval Estimation: Methods of finding interval estimators; Inverting to a test statistic, pivotal quantities, pivoting the cumulative density function, Bayesian interval.Method of evaluating interval estimators;  size and coverage probability, test related to optimality, loss function optimalityHypothesis test: Simple hypothesis, composite hypothesis, Neyman-Pearson lemma, uniformly most powerful test, likelihood ratio test, the sequential probability test, Bayesian testing procedures Teaching Methods: Lecture demonstration and tutorial discussions Assessment/ Evaluation Details: In-course assessments              30%End of course Examination      70% Recommended Readings: Casella, G., and Berger. R., Statistical Inference, 2nd Edition, Pacific Grove, CA: Wadsworth, 2001.Knight, K., Mathematical Statistics, 1stEdition, Chapman and Hall/CRC, 1999.Hogg, V., McKean, W., and Craig, T., Introduction to Mathematical Statistics, 7th Edition, Pearson, 2012.Bickel, P. J., and Doksum, K. A., Mathematical Statistics: Basic Ideas and Selected Topics, 6th Edition, San Francisco: Holden-Day, 1977.

STA406M3: Multivariate Analysis II

 Course Code STA406M3 Course Title Multivariate Analysis II Academic Credits 03 Prerequisite Hourly Breakdown Theory Practical Independent Learning 45 Hours – 105 Hours Objective: Introduce further multivariate techniques and their application to real world problems Intended Learning Outcomes: Use principal component analysis effectively for data exploration and dimension reductionApply factor analysis effectively for exploratory and confirmatory data analysisApply multivariate regression to real world data Classify the groups using discriminate functionApply discriminate function among groupsFind groupings and associations using cluster analysis Syllabus Outline Course Contents: Principal Component Analysis: Derivation of principal components: Covariance matrix and Correlation matrix, loading matrix, Scree plot, principal component scores.Factor Analysis:Orthogonal factor model, Methods of Estimation: Principal Component Method and Maximum Likelihood Method, Factor Rotation: Graphical method, Varimax and Oblique rotation, Factor Scores.Multivariate regression:Multivariate linear regression model, Assumptions of multivariate linear regression, Least squares method ofparameter estimation, Statistical Inference on regression coefficients.Canonical Correlation Analysis: Canonical variates and canonical correlation, test for significant canonical correlationDiscrimination and Classification: Separation and Classification for two population, Fisher’s Discriminant function, Classification with several population.Cluster analysis: Similarity measures: Pairs of items and Pairs of variables, Clustering methods: Single Linkage, Complete Linkage, Average Linkage and K-mean method Teaching Methods: Lecture demonstration and Tutorial discussions Assessment/ Evaluation Details: In-course assessments            30%End of course Examination     70% Recommended Readings: Chatfield, C.and Collins, A. J., Introduction to multivariate analysis, New York: Chapman and Hall, 1980.Johnson, R. A.and Wichern, D. W., Applied multivariate statistical analysis, Englewood Cliffs, N.J: Prentice Hall, 1992.Everitt, B.S. andHothorn, T., An Introduction to Applied Multivariate Analysis with R, Springer, 2011.

 Course Code STA407M4 Course Title Advanced Probability Theory Academic Credits 04 Prerequisite PMM202G2 and PMM203G3 Hourly Breakdown Theory Practical Independent Learning 60Hours _ 140 Hours Objectives: Introduce basic concepts of probability theory in measure theoretic approachDevelop clear ideas on the concept of integration in probability measure space and the expectation of random variablesImpart profound knowledge and application methods on distribution functions, mode convergence and characteristic functionsProvide sound theoretical basis for further studies in mathematical statistics Intended Learning Outcomes: Recall the concepts of probability theoryConstruct probability measures and measurable spacesIllustrate the properties of random variables and expectationFormulate integrals with respect to probability measuresExpress probability and moment inequalitiesDiscuss the modes of convergenceApply Fatou’s lemma, monotone and dominated convergence theoremsExplain Borel-Cantelli lemmas and Kolmogorov zero-one lawDiscuss the properties of distribution functions and characteristic functionsExplain weak and complete convergence of sequence of distribution functionsApply decomposition theorem, Helly-Bray lemma and theorem, uniqueness theorem, inversion theorem, Levy continuity theorem and central limit theorem Syllabus Outline Contents: Mathematical Foundation of Probability Theory:Sets and Operations, Collection of sets, Algebra and Sigma-algebras of sets, limits of sets, monotone sequence of sets, Probability spaces and properties, Construction of a probability measures and continuity theorem, Conditional probability and Independent events, Borel sets.Random Variables:Basic properties of random variables and vectors, random elements, induced probability measures and spaces, measurability and limits, Functions of random variables, simple random variables, induced sigma-algebras.Expectation and Convergence:Definitions and Properties of Expectation, Convergence concepts; Uniformly and point-wise, Mode of convergence; almost surely, in probability, in rth mean, in distribution. Convergence of function of random variables, Markov and Chebyshov’s inequalities. Moment Inequalities: Holder’s, Minkowski and Jensen’s. Fatou’s Lemma, Monotone and Dominated Convergence Theorems, Product measures. Independence of function of random variables and sigma algebras. Borel-Cantelli Lemmas, Kolmogorov zero-one Law, Strong Law of Large Numbers.Distribution Functions: Properties of distribution functions, Decomposition theorem, weak and complete convergent, Helly-Bray lemma, extended lemma and theorem, Convolution, Conditional Distributions and Expectations.Characteristic Functions: Definition and Basic Properties, Uniqueness theorem, Inversion theorem, Levy Continuity theorem, Examples of Characteristic functions, Law of Large Numbers, Stirling’s formula, Central Limit Theorem, Martingales. Teaching Methods: Lectures, Tutorial discussion, Handouts, Use e-resources Assessment/ Evaluation Details: In-course Assessments:             30%End-of-course Examination:     70% Recommended Readings: Alan F. Karr., Probability, 1st Edition; Springer-Verlag New York, Inc, 1993.Ramdas Bhat. B., Modern Probability Theory, An Introductory Text Book,2nd Edition, Wiley Eastern Limited, 1985.Kai Lai Chung. ,A Course in Probability Theory. 3rd Edition, Elsevier (USA), 2000.Clarke. L. E.,Random Variables, 1st Edition, Longman Mathematical Texts, USA by Longman Inc., New York, 1975.Allan Gut., Probability: A Graduate Course. II. series, Springer texts in Statistics, Springer-Verlag New York, Inc, 2005.

STA408M3: Theory of Linear Models

 Course Code STA408M3 Course Title Theory of Linear Models Academic Credits 03 Prerequisite Hourly Breakdown Theory Practical Independent Learning 45 Hours – 105 Hours Objective: Provide depth knowledge in theory of linear models and its applications Intended Learning Outcomes: Prove basic results related to the statistical theory of linear modelsDiscuss different type of parameter estimation in linear modelsPerform hypothesis testing related to different characteristics of a linear modelAssess the fit of a linear model to data and the validity of its assumptionsDevelop theoretical knowledge on the  concepts behind the robust regression Syllabus Outline Contents: IntroductionMultivariate Normal Distribution, Distribution of Quadratic forms,  Estimation by Least Squares, Orthonormal Bases, Q-R decompositions, Hat MatricesVariances and CovariancesGauss- Markov Theorem,  Estimation of variance, Generalized Least Squares, Collinearity in Least square estimation, Consequences and Identification, Biased Estimation, Ridge Regression, Sensitivity Analysis of Least Squares using ResidualsStatistical Inference for Normal ErrorsChi-square, t and F distributions, Distribution theory, Hypothesis testing, Robustness of F-tests, Non-central Chi-square and Power of tests, Power and Size of F-testsNon-Full Rank ModelsAnalysis of Variance Models, Singular Value Decompositions, Estimable Functions and their properties, Hypotheses testing, Analysis of Variance Models with CovariatesRobust RegressionInfluence Curves, Sensitivity Analysis based on the Influence Curve, M-Estimation, GM- Estimation, Influence curves of estimators (GLS and GM) Teaching Methods: Lecture demonstration, and tutorial discussions Assessment/ Evaluation Details: In-course assessments              30%End of course Examination     70% Recommended Readings: James H. Stapleton,Linear Statistical Models, John Wiley and Sons, 2009.George, A. F. Seber and Alan, J. Lee, Linear Regression Analysis, secondEdition, John Wiley and Sons, 2011.Alvin, C. Rencher and Bruce Schaalje,G., Linear Models in Statistics, Second Edition, John Wiley and Sons, 2007.Cook, R.D and S. Weisberg, S., Residuals and Influence in Regression, Taylor and Francis, 1982.John Fox., Regression Diagnostics, Sage Publications, 1991.

STA409M6: Research project

 Course Code STA409M6 Course Title Research Project Academic Credits 06 Hourly Breakdown Theory Practical Independent Learning – – 300 Hours Objective: Provide training in scientific skills of problem analysis, research design, evaluation of empirical evidence and dissemination. Intended Learning Outcomes: Identify a research problemList appropriate literature to discuss the research findingsPlan a proper research methodologyFormulate a suitable hypothesis for the research problemApply suitable statistical techniques to make decisionsDevelop skills of scientific writing and presenting results Syllabus Outline Course Description: Students are expected to carry out an independent research project in the field of Statistics under the supervision of a senior staff member in the department. Students need to give presentations in the beginning, middle, and the end of their research. At the completion of the research project, students are expected to write a comprehensive report. During the research, students are expected to maintain a research diary. Teaching Methods: Guided independent study, Discussion with the supervisor, Use of e-resources Assessment/ Evaluation Details: Presentation               30%Project Report        70% Recommended Readings: Kothari, C. R., Research Methodology: Methods and Techniques, Second Edition, New Age International (P) Limited, Publishers, 2004.McMillan, K. and Weyers, J., How to Write Dissertations and Project Reports, Prentice Hall, 2011.Denicolo, P. and Becker, L., Developing a Research Proposal. SAGE Publications, 2012.

STA410M2: Bayesian statistics

 Course Code STA410M2 Course Title Bayesian Statistics Academic Credits 02 Prerequisite STA201G3 and STA204G2 Hourly Breakdown Theory Practical Independent Learning 30Hours _ 70 Hours Objectives: Introduce the basic concepts of Bayesian theory.Apply Bayesian statistics in a real world problem. Intended Learning Outcomes: Distinguish classical and Bayesian approachesRecall various priors such as conjugate, non informative, Jeffreys’Determine the posterior and predictive distributions for standard prior distributionsFind mean and variance for the posterior distributionsEvaluate Bayes’ estimate for the parameter of the posterior distributionConstruct the credible interval and highest posterior density intervalTest the simple hypotheses using Bayes’ factorFormulate the linear hierarchical modelsUtilize the Bayes’ risk to select the best decisions Syllabus Outline Contents: Fundamentals of Bayesian Analysis:Definitions of classical and Bayesian approaches to inference about parameters. Bayes’ theorem for parametric inference, likelihood functions, exponential families and conjugate priors. Mixtures of conjugate priors, Non informative priors, Jeffreys’ prior. Prior and Posterior analysis of standard distributions; binomial-beta, Poisson-gamma, exponential-gamma, uniform-Pareto, normal(mean)-normal, normal(precision)-gamma, normal(mean and precision)–normal-gamma. Predictive distributions. Exchangeability, Point and interval estimations; maximum a posteriori (MAP) estimators, credible intervals and highest posterior density intervals. Bayes’ factors, Bayesian hypothesis testing. Two sample problems.Bayesian Linear Models:Uniform priors, Normal priors, Hierarchical models; Two and Three stage models.Statistical Decision Theory:Loss functions, Bayes’ risk, Bayes’ rule, Minimax and Bayes’ procedures. Teaching Methods: ·        Lectures, Tutorial discussion, Handouts, Use e-resources Assessment/ Evaluation Details: In-course Assessments:             30%     End-of-course Examination:     70% Recommended Readings: PeterM. Lee., Bayesian Statistics: An Introduction. 4 th edition, John Wiley and Sons Limited. U.K.,2012.Peter D. Hoff., A First Course in Bayesian Statistical Methods. Springer-Heidelberg London, New York, 2009.Vladimir P. Savchuk and Chris P. Tsokos., Bayesian Theory and Methods with Applications. Atlantis Press, 8, square des Bouleaux, 75019 Paris, France, 2011.James O. Berger., Statistical Decision Theory and Bayesian Analysis. Second Edition, Springer-Verlag, New York, 1988.

STA411M3: Multivariate Analysis I

 Course Code STA411M3 Course Title Data Mining Academic Credits 03 Prerequisite Hourly Breakdown: Theory Practical Independent Learning 45 – 105 Objectives: Provide knowledge on the concepts behind various  data mining techniques and techniques for learning from data as well as data analysis and modelling Intended Learning Outcomes: Plan pre and post-processing operations for data miningDescribe a range of supervised and unsupervised learning algorithmsUse machine learning algorithms on data to identify new patterns or conceptsEvaluate the performance of learning algorithms Course Contents: Introduction to data mining: Data mining and its applications; Data handling–instances, attributes and their typesData mining process: Data preparation/cleansing, sparse data, missing data, inaccurate values, task identification, use of Weka toolSupervised learning: Introduction to classification and regression, rule-based learning, decision tree learning, Naive Bayes, k-nearest neighbour, support vector machines, neural networks, linear regressions, introduction to boostingUnsupervised learning: K-means clustering, Gaussian mixture models (GMMs), Hierarchical clustering, Latent Dirichlet Allocation(LDA)Dimensionality reduction: Principal Component Analysis, Multidimensional Scaling, Filter methodsEvaluation of learning algorithms: Training and testing, Error rates, over- and under- fitting, Cross-validation, Confusion matrices and ROC graphs Teaching/Learning Methods: Lecture demonstration, and tutorial discussions and laboratory experiments Assessment Strategy: In-course Assessments                  30%End-of-course Examination         70% References: Bishop,C. M,  Pattern Recognition and Machine Learning, 2007.Duda. R. O, Hart,P. E. and Stork, D. G., Pattern Classification, 2ndEdition., Wiley, 2000.Mitchell, T., Machine Learning, McGraw Hill, 1997.Witten, I. H., Frank, E. and Hall, M. A, Data Mining: Practical Machine Learning Tools and Techniques, 3rdEdition, Morgan Kaufmann Series, 2011.

STA412M3: Biostatistical techniques

 Course Code STA412M3 Course Title Biostatistical Techniques Academic Credits 03 Hourly Breakdown Theory Practical Independent Learning 45 Hours – 105 Hours Objective: Introduce the applied Biostatistical techniques used in statistical collaboration with various clinical trials. Intended Learning Outcomes: Distinguish kinds and source of dataHow to apply best tools and approaches for data collection or retrievalIdentify pitfalls and best practices for turning data into analyzable dataExamine the data qualitiesIdentify the correct use of models under different response domains Use observational data for comparative studiesDiscuss different types of follow-up and time to event responsesApply basic actuarial and parametric approaches for time to event responsesOutline different types of follow-up and longitudinal dataDevelop basic modeling approaches for longitudinal response Course Contents: Data: Kinds of raw data: Unstructured, semi-structured; structured; Sources of data: active versus passive data, clinical databases, registries, administrative data; Data Collection tools: spreadsheets, databases, text mining; Analysis dataset: event-based, longitudinal, unique record versus multiple records; Data screening: manual review, descriptive summary, exploratory data analysis; best practices when using tables and figures.Study Initiation: Introduction to types of studies; power calculation; measures of agreement: kappa statistic, concordance correlation coefficient; diagnostic tests: sensitivity, specificity, positive predictive value, negative predictive value; Simple Statistical Tests: parametric and nonparametric tests: comparison tests, trend tests, tests for correlated responses and assumptions.Modelling:Understand the basic principles of different kinds of statistical models, and their applicability to the analysis of clinical data; Models for continuous Response, Categorical Response, Count data, Zero-inflated data; Methods used in comparative studies: weighting, stratification, adjustment, matching.Time related responses: Introduction to Time to Event data: left censored data, competing risk data, repeated events; Introduction to Longitudinal Responses: continuous, binary, ordinal and nominal. Brief introduction to marginal and conditional (mixed-effects) models.Machine Learning Methods: Use of Bootstrap to estimate standard errors and confidence interval, Introduction toRandom Forests: continuous response, categorical response, and time to event response. Teaching Methods: Lecture demonstration, Quizzes and Tutorial discussions Assessment/ Evaluation Details: In-course assessments             30%End of course Examination     70% Recommended Readings: Forthofer, R. N., Lee, E. S. and Hernandez, M., Biostatistics: A Guide to Design, Analysis and Discovery, 2nd Edition, Elsevier- Academic Press, Boston, 2007.Gordis, L., Epidemiology, 5th Edition, Elsevier- Academic Press, Philadelphia, 2014.Harrell, F.E., Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis, 2nd Edition, Springer, New York, 2001.