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:  
 
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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:  
 
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Teaching Methods:  
Lectures and Tutorial discussions  
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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:  
 
Course Contents:  
Threeway Contingency tables; Conditional versus marginal tables, Simpson’s paradox, Conditional versus marginal odds ratios, Conditional versus marginal independence, CochranMantelHaenszel (CMH) test Homogeneous association for tables.
 
Teaching Methods:  
Lectures and tutorial discussions  
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Course Code  STA304M3  
CourseTitle  Computational Statistics  
Credit Value  03  
Hourly Breakdown  Theory  Practical  Independent Learning 
15  60  75  
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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  
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Teaching Methods:  
Lectures, demonstration and Tutorial discussions  
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Level – 4M
Course units effective from academic year 2016/2017 to date
Course Code  STA401 M4  
Course Title  Measure Theory  
Credit Value  04  
Prerequisites  PMM202G2 and PMM203G3  
Hourly Breakdown  Theory  Practical  Independent Learning 
60  —  140  
Objectives:  
 
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Course Contents:  
Measure Spaces:Preliminaries:Algebra and σalgebras of sets,Borel sets; Lebesgue measure: Outer measure, Measurable sets, and Lebesgue measure,Properties,Example of a nonmeasurable 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 σalgebras, Carathéodory’s theorem, and LebesgueStieltjes integral. Product Measure:Measurable rectangle, Semialgebra, Construction of product measures, Fubini’s theorem, and Tonelli’s theorem Differentiation and Integration:Differentiation of monotone functions: Vitali’s lemma, Functions of bounded variations; Differentiation of an integral: Indefinite integral, and Absolutely continuous functions.  
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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  
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Contents:  
 
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Laboratory practical  
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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:  
 
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Syllabus Outline  
Contents:  
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 pure jump process, ChapmanKolmogorov 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.
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.  
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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.  
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Syllabus Outline  
Contents:  
Estimation 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 autocorrelations
Poisson 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 Quasilikelihood (GQL) Approach
Binary mixed models and basic properties: Computational formulas for binary moments; Estimation for single random effect based parametric mixed models: Method of moments, Generalized Quasilikelihood approach, Maximum likelihood estimation (MLE)
Marginal 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 models
Marginal model; Marginal model based estimation of regression effects; Some selected correlation models for longitudinal binary data; Loworder autocorrelation models for stationary binary data: Binary AR(1) model, Binary MA(1) model, Binary EQC model; Inferences in Nonstationary correlation models for repeated binary data  
Teaching Methods:  
Lecture demonstration, and tutorial discussions  
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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  
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Lecture demonstration and tutorial discussions  
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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  
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Lecture demonstration and Tutorial discussions  
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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:  
 
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Syllabus Outline  
Contents:  
Mathematical Foundation of Probability Theory: Sets and Operations, Collection of sets, Algebra and Sigmaalgebras 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 sigmaalgebras. Expectation and Convergence: Definitions and Properties of Expectation, Convergence concepts; Uniformly and pointwise, 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. BorelCantelli Lemmas, Kolmogorov zeroone Law, Strong Law of Large Numbers. Distribution Functions: Properties of distribution functions, Decomposition theorem, weak and complete convergent, HellyBray 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.  
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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  
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Syllabus Outline  
Contents:  
Multivariate Normal Distribution, Distribution of Quadratic forms, Estimation by Least Squares, Orthonormal Bases, QR decompositions, Hat Matrices
Gauss 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 Residuals
Chisquare, t and F distributions, Distribution theory, Hypothesis testing, Robustness of Ftests, Noncentral Chisquare and Power of tests, Power and Size of Ftests
Analysis of Variance Models, Singular Value Decompositions, Estimable Functions and their properties, Hypotheses testing, Analysis of Variance Models with Covariates
Influence Curves, Sensitivity Analysis based on the Influence Curve, MEstimation, GM Estimation, Influence curves of estimators (GLS and GM)  
Teaching Methods:  
Lecture demonstration, and tutorial discussions  
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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.  
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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 eresources  
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Course Code  STA410M2  
Course Title  Bayesian Statistics  
Academic Credits  02  
Prerequisite  STA201G3 and STA204G2  
Hourly Breakdown  Theory  Practical  Independent Learning 
30Hours  _  70 Hours  
Objectives:  
 
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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; binomialbeta, Poissongamma, exponentialgamma, uniformPareto, normal(mean)normal, normal(precision)gamma, normal(mean and precision)–normalgamma. 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 eresources  
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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:  
 
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Teaching/Learning Methods:  
Lecture demonstration, and tutorial discussions and laboratory experiments  
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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:  
 
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Teaching Methods:  
Lecture demonstration, Quizzes and Tutorial discussions  
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