University of Mines and Technology(UMaT), Tarkwa. Ghana

20.5.3    Masters Programme in Statistics

a)    Core and Compulsory Modules

The MSc. coursework comprises four (4) core/compulsory modules namely:

•    Research Methods (MA 501)

•    Computer Programming (MA 507)

•    Statistical Inference (MA 523)

•    Operations Research (MA 505)

In addition, a minimum of three other modules must be selected by the candidate in consultation with his/her Supervisor(s). Applicants without adequate Mathematics or Statistics background will be required to register for the module in Optimisation Techniques and Computer Applications.

b)    Content of Modules

First Semester

Second Semester

First Semester

MA 277 Probability and Statistics
Credits: 0

Random variables and probability distributions: expectations and variances of random variables, properties. Moments and moment generating functions. Some special discrete distributions: Bernoulli, binomial, geometric, negative binomial, Poisson and multinomial distributions. Some special continuous distributions: uniform, exponential, Gaussian, gamma, beta, chi-squared and other related distributions. Joint probability distributions: properties, marginal and conditional distributions. Conditional mean and variance

MA 501 Research Methods
Credits: 3

Introduction to research: Research project formulation/management, the research process, literature review and organization. Epistemology and its implications for research methodology and design. Theoretical framework (variable definition and generation of hypothesis). Scientific research design (differences between qualitative and quantitative methodology, measurement issues: reliability and validity). Qualitative data collection (e.g. in-depth interviews, focus groups, observations). Analysis of qualitative data. Principles of quantitative data analysis (descriptive statistics). Quantitative methods ( hypothesis testing, inferential statistics). Sampling, questionnaire design and methods for pre-testing. Research proposal for competitive research grant. Research presentation (formatting dissertation). Case studies.

MA 505    Introduction to Operations Research
Credits: 3

Introduction to Deterministic methods for Optimization, with focus on mathematical programming (linear, nonlinear, integer) and network methods. Introduction to probabilistic methods for modeling and analyzing the performance of complex systems. Topics include Markov chains, queuing, forecasting, discrete event simulation and inventory modeling.

MA 507    Computer Programming
Credits: 3

Input and output procedures. Elementary mathematical functions . User defined functions. Relational and logical operators. Conditional statements . Looping and the switch structure. Solution of Linear and non linear algebraic equations. Application to differential equations. Symbolic processing with MATLAB.

MA 523    Statistical Inference
Credits: 3

Elements of Theory of statistical games and decision. Reduction of decision problems into problems of statistical inference. Admissibility and completeness. Methods of estimation. Lehman Scheffe Theorem. Invariance. Confidence sets. Large sample theory for confidence bound. Construction of tests: MP, UMP and likelihood ratio criterion with their applications.

MA 525    Design and Analysis of Experiments
Credits: 3

General Linear Models; Generalized inverse of a Matrix, Factorial Experiments: Symmetric and Asymmetric; Balanced and Partially Balanced incomplete Block Designs, Resolvable, Group Divisible, Connected, Lattice Designs. Row – Column Designs; Latin Square, Lattice, Cross Over Design. Response Surface Methodology, Construction of Designs.

MA 527 Multivariate Analysis
Credits: 3

Fundamental Theory of Matrices and their properties. Multivariate Normal Distribution and associated multiple and partial correlation and regression theory. Estimation of parameters. Hotelling’s T2 and Mahalanobis D2 Wishart distribution. Tests concerning mean vectors and variance and associated confidence bounds. Some other multivariance distributions.

MA 529    Analysis of Categorical Data
Credits: 3

Probability models for (2 × 2) tables. Measures of association for (2 × 2) tables. Probability models for (s × r) tables. Goodness of fit tests. Squares tables and their applications. Structural models for two and higher dimensions. Iterative proportional fitting of log models. Complete and in- complete multiway table. Quasi symmetry.
MA 531    Time Series and Forecasting
Credits: 3

Basic concepts: definitions, basics of time Series analysis, types of time series. Components of time series: Trend, seasonality, cycle variations, etc. Trend analysis: moving averages, exponential smoothing, autoregressive and partial autoregressive functions. Use of SPSS.

Second Semester

MA 500 Thesis
Credits: 12

The thesis must be an embodiment of independent research work under the guidance of Supervisor(s) on a topic of the student’s area of specialization. A thesis embodying the results of the research will be presented to the Department for assessment. A panel of examiners will assess the thesis.

MA 516     Computational Methods in Optimization
Credits: 3

Optimization Problems. Examples of Optimization problems. The Optimization in one dimension. Iterative methods of Optimization. Least squares procedures for solving equations, contraction mapping theorem. Newton’s methods. Steepest Descent Methods, Conjugate direction Methods in R, Conjugate Gradient Method Algorithm, Projection Methods.

MA 522     Econometric Methods
Credits: 3

Ordinary least squares (OLS), Gauss – Markoff Theorem. Maximum likelihood estimation (MLE) specification and mis-specification test. Predictive and non – predictive tests; Tests of hypotheses in the linear model. The likelihood ratio, the Waid and the Language multiplier tests, Multi – collinearity. Specification bias. GLS. Dummy variables and seasonal variations. Inferences about linear model based on asymptotic distribution theory.

MA 524    Stochastic Processes with Applications
Credits: 3

Classification of stochastic processes, Random walk models, discrete queueing chain, inventory model, branching processes, Poison, Birth and Death Processes, waiting time models, Guassian processes, Martingales, Mean covariance and sample functions. Integration and differentiation of SPs. Estimation problems.

MA 526    Quality Control and its Management
Credits: 3

Objectives of statistical quality control specifications and tolerance limits, control charts. Acceptance sampling. Use of various military standards. Dodge rooming system for lot by lot acceptance sampling. AQL/AOQL criteria for acceptance sampling. One stage, two-stage, multi-stage sampling. Inspection plan, case studies. Quality control practice in Japan, America and Britain, recent quality movement. Management-by-objective. Its shortcomings including problem of performance appraisal. Importance of quality management to company survival.

MA 528    Sample Surveys
Credits: 3

Use of auxiliary information; multivariate ratio, regression and difference estimators and their extension to double sampling procedure. Quenouille’s technique of bias reduction. Sampling on successive occasions. Non–sampling Errors. Some specialized sampling techniques.

MA 530 Postgraduate Seminar
Credits: 3

Students will be required to make at least two presentations on the progress and research underway in their areas of specialisation. This will be assessed by a Departmental Panel. Postgraduate students are required to attend the seminar(s).