MPhil

MPhil Actuarial Science

enaidoo — Fri, 11 Sep 2020 20:14:50 +0000

MPhil Actuarial Science enaidoo Fri, 09/11/2020 - 20:14

Overview

Graduates’ skills can be applied in industry as Actuarial, Statistical, and high caliber Financial and Risk Analysts, just to mention a few. Such employment opportunities of the graduates of this programme will help in the design and operation good and viable National Health Insurance and Pension Schemes. The financial industry of Ghana will also benefit from the skills necessary for company strategic development and planning, financial product development, pricing and valuation of a wide variety of products in various sectors of the economy. In the academia, the programme also aims at providing a foundation for graduate studies in areas such as Actuarial Science, Statistics, Decision Science, Operations Research, Computational Finance and Risk Management, and Financial/Quantitative Finance who will in turn contribute to teaching and research in our tertiary institutions

Aims and Objectives

The MPhil degree programme in Actuarial Science seeks to develop individuals with a balance between mathematical, statistical, financial, and economic theories, and their applications to practical problems. The programme is designed to provide theoretical as well as applicable education in quantitative aspects of Risk Modelling and Management, Finance and Statistics. Graduates will be capable of abstracting mathematical models for real-world problems and applying appropriate computer-based solutions to them.

The graduates will also have the mathematical, statistical, and business skills needed to determine the expected costs and risks in any situation where there is financial uncertainty and data for creating a model for those unpredictable and unexpected contingencies (risks).

Content of the Courses for each Semester

YEAR 1: SEMESTER 1

ACTS 561: FINANCIAL MATHEMATICS (3, 0, 3)

Introduction to the mathematical theory of interest as well as the elements of economic and financial theory of interest. Topics include rates of interest and discount; simple, compound, real, nominal, effective, dollar (time)-weighted; present, current, future value; discount function; annuities; stocks and other financial instruments; definitions of key terms of modern financial analysis; yield curves; spot (forward) rates; duration; immunization; and short sales. The course will cover determining equivalent measures of interest; discounting; accumulating; determining yield rates; and amortization. Derivative pricing, fixed asset pricing, Neural networks, Valuing by expected utility.

ACTS 563: RISK THEORY (3, 0, 3)

This course covers the Statistical Methods that provide a further grounding in mathematical and statistical techniques of particular relevance to financial work. Topics include; Bayesian Statistics: Bayesian Theorem. Prior and Posterior distributions: Determining the posterior decisions, Continuous prior distributions, Conjugate prior, Improper prior distributions. The loss function: Quadratic loss, Absolute error loss, All – or – nothing loss, Some Bayesian posterior distributions. Loss Distributions: The exponential, gamma, normal, Pareto and generalised Pareto, lognormal, Weibull and Burr distributions. Estimation: The method of Moments and the maximum likelihood estimation of the exponential and gamma, the normal distribution, the Pareto and generalised Pareto, the lognormal and Weibull and Burr distributions. Goodness – of – fit test. Mixture distributions. Reinsurance: Proportional and Non – proportional reinsurance. Reinsurance arrangement: Excess of loss reinsurance – the insurer and the reinsurer. Proportional reinsurance. Particular distributions: Lognormal and normal distribution. Inflation. Estimations. Policy excess. Credibility theory: Credibility premium formula, the credibility factor. Bayesian credibility: Prior parameter distribution, likelihood function, Posterior distribution, loss function. The Poisson/gamma model with numerical illustration. The normal/normal model. The Bayesian approach to credibility. Empirical Bayes credibility theory: Model 1 and 2. Risk Model: Basic Risk Model. Collective Risk Model: Distribution functions and Convolutions. Compound Poisson, binomial and negative binomial distributions. Excess of loss insurance. Individual risk model. Ruin Theory: Surplus process, probability of ruin in continuous and discrete time process. Poisson and Compound Poisson. Probability of ruin in short term. The adjustment coefficient and Lundberg’s inequality and its application.

ACTS 565: Survival and Stochastic Models (3,0,3)

This course covers stochastic processes and survival models and their application. Topics include: Principles of actuarial modelling. Stochastic processes: Markov Chains, The two – state Markov Model, Time – homogeneous jump processes, Time – inhomogeneous Markov jump processes. Survival Models: Estimating the lifetime distributions, Proportional hazards models. The Binomial and Poisson models. Exposed to risk. Graduation and statistical tests. Methods of graduation.

Prerequisite: Calculus and probability

ACTS 567: ACTUARIAL MATHEMATICS I (3,0,3)

This course covers the mathematical and probabilistic structure of life contingent ﬁnancial instruments. It introduces survival models, covers life tables and their applications, life insurance, beneﬁts, lifetime annuities. Topics include; Probability Review, Survival Distributions: Probability functions, force mortality, mortality laws, moments, percentiles and recursions, fractional ages, selected mortality. Insurance: Continuous – Moments, annual and m-thly, moments, probabilities and percentiles, recursive formulas, varying insurances, relationships between Insurance payable at moment of death and payable at end of Year. Annuities: Continuous, Expectation, annual and m-thly, variance, probabilities and percentiles, varying annuities and recursive formulas, m-thly payments. Premiums: Net premiums for fully Continuous Insurances, net premiums for discrete insurances calculated from life tables, net premiums for discrete insurances calculated from formulas, net premiums paid on an m-thly basis, gross premiums, variance of future loss (Continuous), variance of future loss (discrete), probabilities and percentiles of future loss. Reserves: prospective benefit reserve.

ACTS 569: Finance and Financial Reporting (3, 0, 3)

This course covers a basic understanding of corporate finance including a knowledge of the instruments used by companies to raise finance and manage financial risk and to provide the ability to interpret the accounts and financial statements of companies and financial institutions. Topics include: The key principle of finance: Company ownership, Taxation, Financial instruments, Use of derivatives, Issue of shares. Introduction to accounts: The main accounts, Depreciation an reserves, Generating accounts, Group accounts and insurance company accounts, Interpretation of accounts, Limitations of accounts. Financial institutions. Weighted average cost of capital: Capital structure and dividend policy. Capital project appraisal.

MATH 561: MEASURE AND INTEGRATION (3, 0, 3)

Algebras, Measures, Construction of measures, Measurable functions, Construction of the integral, Integral for simple functions, Integral for positive measurable functions, Integral for measurable functions, Convergence theorems and applications, The three main convergence results, Consequences and applications, Lp-spaces, Minkowski and Holder's inequalities, Completeness of Lp, Lp-spaces on intervals, Applications to Fourier series Introduction of Fourier Series, Fourier coefficients, Fourier series in , Fourier series.

Year 1 Semester 2

ACTS 562: FINANCIAL ECONOMICS (4, 0, 4)

The course covers asset-liability models and to how value financial derivatives. These skills are also required to communicate with other financial professionals and to critically evaluate modern financial theories. Topics include: The efficient markets hypothesis, Utility theory and stochastic dominance. Measurement of investment risk. Portfolio theory. Models of asset returns. Asset pricing Models. Brownian motion and Martingales. Stochastic calculus and Ito processes. Interest rate models: Vasicek and Cox-Ingersoll-Ross bond price models, Black-Derman-Toy model binomial model matching in a given time zero yield curve and a set of volatilities:Rational Valuation of Derivative securities: Use put-call parity to determine the relationship between prices of European put and call options and to identify arbitrage opportunities. Computation of European and American options using Binomial and Black-Scholes option-pricing models, Calculation and interpretation of option Greeks, Cash flow characteristic of exotic options; Asian, Barrier, Compound, Gap and Exchange, Stock prices and Diffusion Process, Ito’s Lemma in one dimensional case and Option pricing concepts to Actuarial problems such as equity-linked insurance, Risk Management Techniques: Control of risk using the method of delta-hedging. Credit Risk.

ACTS 564: Statistical Modelling (3, 0, 3)

This course covers the Statistical Methods that provide a further grounding in mathematical and statistical techniques of particular relevance to financial work. Topics include; Decision Theory: zero – sum two player games-domination, the minimax criterion-saddle points, and Randomized strategies. Statistical games. Decision criteria: the minimax criterion, the Bayes criterion. Generalized linear Models: Exponential families: normal, Poisson and binomial distributions. Link functions and linear predictors, Deviance of model fitting. Run – off triangles: Estimating future claims. Projection using development factors. Chain – ladder method. The inflation adjusted chain ladder. The Bornhuetter – Fergusson Method. Time series. Monte Carlo simulation.

ACTS 566: Economics for Actuaries (3, 0, 3)

This course covers fundamental concepts of micro and macroeconomics as they affect the operation of insurance and other financial systems. Topics include: Economics concepts: Demand and supply, Elasticity and uncertainty, Consumer demand and uncertainty, Production and costs, Revenue and profit. Perfect competition and monopoly: Imperfect competition, Products, marketing and advertising, Growth strategy, Pricing strategies. Government intervention in markets: Government and the firm. Supply – side policy. International trade. The balance of payments and exchange rates. The macroeconomic environment. Money and interest rates. Business activity, unemployment and inflation. Demand – side macroeconomic policy.

ACTS 568: ACTUARIAL MATHEMATICS II (3,0,3)

Decrements modeling and their applications to insurance and annuities, non-stochastic interest rate models to calculate present values and annuities. Models for cash flows and non-interest sensitive insurances other than traditional life insurances and annuities. Models for contract cash flows for basic universal life insurances. Models for cash flows of basic universal life insurance. Calculate the benefit reserve. Models that consider expense cash flows. Calculate an expense factor using the appropriate exposure. Calculate probabilities and moments of the present-value-of-expenses random variable based on single decrement on single life model and multiple decrements on a single life models. Modeling of expense reserve. Calculate a gross premium given expenses and benefits based on: the equivalence principle; and a return on gross profits basis. Modeling gross premium reserve. Modeling of asset share. Severity Models: compute the basic distributional quantities such as moments, percentiles, generating functions: Frequency Models, Aggregate Models: compute relevant parameters and statistics for collective risk models, evaluate compound models for aggregate claims, compute aggregate claims distributions.

ACTS 572: Investment and Asset and Liabilities Management (ALM) for Actuaries (3, 0, 3)

This course develops an understanding of the fundamental concepts of Investment and Asset Liability Management (ALM) for actuaries. A basic knowledge of financial mathematics is assumed. This course is an elective course, which provides students with the knowledge to apply in a practical sense the theoretical framework that they learned from the foundational actuarial examinations. Topics to be considered are Investment and valuation, general principles of asset allocation, Investment risk, Portfolio selection techniques and Investment modeling, asset and liability modeling.

ACTS 574: PENSION MATHEMATICS (3, 0, 3)

This course focuses on fundamental issues of pension mathematics. The course content focuses on pensions system in Ghana, pension mathematics and investment of pension fund. Topics include: Introduction of pension systems in Ghana and pension plan benefits. Objectives of pension mathematics and fundamental structure. Actuarial assumptions which include decrement assumptions, salary assumptions and interest rate assumptions. General theory for funding method. Funding method used for actual pension management. Practical actuarial valuation to check appropriateness of actuarial assumptions.

ACTS 578: Predictive Analytics (3, 0, 3)

Predictive Analytics Problems and Tools, Problem definition, Data Visualization, Data Types and Exploration, Data Issues and Resolution, Generalized Linear Models, Decision Trees, Cluster and Principal Component Analysis, Communication.

ACTS 580: General Insurance Reserving and Capital Modelling Principles (3, 0, 3)

General insurance products and general business environment: types of general insurance for customer needs, the financial and other risks they pose for the general insurer including their capital requirements and possible effect on solvency. the main features of the general insurance market, the effect of different marketing strategies, fiscal regimes, inflation and economic factors, legal, political and social factors, professional guidance and the impact of technological change. Risk, uncertainty and regulation: the major areas of risk and uncertainty in general insurance business with respect to reserving and capital modelling, in particular those that might threaten profitability or solvency. Purposes of regulating general insurance business. Reserving: with regard to reserving work using triangulations, appropriate reserving bases for general insurance business, stochastic reserving processes. Capital modelling: Evaluate the following approaches to capital modelling; deterministic models, stochastic model. Assess capital requirements for the following risk types; insurance, market, credit, operational, liquidity and group risk. Data, investigations, reinsurance and accounting: With regard to the use of data in reserving and capital modelling, the principles of investment, the asset liability matching requirements of a general insurer, develop an appropriate investment. Strategy, the methods and principles of accounting for general insurance business and interpret the accounts of a general insurer, the changes to accounting methods expected under IFRS.

Programme Type

MPhil

MPhil. Mathematical Statistics

enaidoo — Fri, 11 Sep 2020 20:01:14 +0000

MPhil. Mathematical Statistics enaidoo Fri, 09/11/2020 - 20:01

Overview

Many laboratories, both government and private, maintain independent research staffs that include statisticians. Their work often deals with the development of new technology, including design and analysis of experiments, software development, and numerical simulation, such as weather and climate forecasting, which depends heavily on the use of supercomputers. Another major reason for studying statistics at higher level is to pursue a career in teaching. However, the turn out of the training fails to meet the minimum demand. Mathematics and Statistics departments of Universities are encountering a growing gap between supply and demand of faculty. Dwindling numbers of students are entering in graduate study in Statistics, resulting to a bumper crop of faculty retirees. These trends need to be reversed. Rising public concern has gradually driven teachers’ salaries upward, and there is renewed interest in teaching as a career among graduates of undergraduate programmes in mathematical sciences.

Graduate study in Statistics thus becomes essential. The undergraduate training provides a foundation upon which more advanced statistics courses will be built. In graduate study, one or two further years of coursework completes this basic training. Thereafter, more specialized courses, often at the frontiers of research, are taken. Applied Statistics students take courses in various application areas to acquire experience in modeling the real world, and to learn how statistics coupled with mathematics solve problems from the physical and biological sciences, and in risk management as well.

The breadth and depth of Statistics graduate programme prepares the students for managerial positions in government, business, and industry and research work that will lead to publication of theses, enrolment in a PhD study, employment in research institutions as faculty. The diversity of applications is an exciting aspect of the field and is one reason why the demand for well-trained statisticians continues to be strong. This is in line with the department’s graduate training of students to formulate abstract mathematical models for real-world problems and also design and apply appropriate computer-based solutions to real world problems.

The programme emphasises on the teaching of theory and principles of mathematics, statistical theory and methodology, and applications to provide the basis for meaningful practical applications. The field exercise components of the programme are meant to give the students a chance to work in groups on real and practical issues. Important components of the programmes are the courses on sample surveys, operation research, and statistical quality control, where students plan, prepare, and conduct their own surveys/experiments under supervision of teaching staff. Statistical skills learned through lectures and laboratory works are put also put into practice during industrial attachment and also writing of their theses in the second year.

Aims and Objectives

The MPhil (Mathematical Statistics) emphasizes a broad, solid foundation in techniques and underpinnings of probability theory and statistical modeling. Its focus on breadth and depth is intended to produce well-rounded, knowledgeable scholars. This concentration is excellent preparation for academic positions in mathematical statistics and industrial or governmental positions that require broadly trained statisticians with a strong understanding of statistical theory.

The programme also emphasizes the theory and application of a broad array of statistical models, such as linear, generalized linear, nonlinear, categorical, spatial, correlated response, and nonparametric regression models. This prepares students to specify and choose appropriate models; fit the models using available statistical software; and make sound statistical conclusions and interpretive statements. It is excellent preparation for students interested in academic, industrial, or government positions that involve data modeling and analysis.

Specifically the programme will:

Provide a solid training in mainstream advanced statistical modelling
Expose students to modern developments in Statistics
Be flexible in allowing the student to take a broad range of options, including modules within financial mathematics, and measure theory
Reflect the research interests of the Department of Mathematics including specialised topics in statistical shape analysis and directional data, and stochastic financial modelling.
Enable students pursue a PhD study in Mathematical Statistics.
Give the graduates of this programme an appropriate combination of statistical and industrial systems backgrounds so that they may have successful technical careers in industry or successful careers doing research in industrial statistics.
Train academic industrial statisticians who can serve as better bridges between the academic and corporate worlds.

Course Contents for each Semester

YEAR ONE: SEMESTER ONE

MSTAT 573: Mathematical Statistics (3, 2, 4)

This will deepen mathematical understanding of Statistical inference as well as decision theory. Topics to be covered include the following: Order statistics; Theory of estimation: Criteria of estimation, sufficiency, completeness, uniqueness and exponential class probability density functions, Cramer-Rao inequality and methods of estimation; Statistical hypotheses testing: Review of significance test, Power function, losses and risks, most powerful, generalised, likelihood ratio, conditional and sequential tests; Decision theory: Basic concepts, decision criteria, minimax and Bayesian estimation criterion. Non-parametric statistics: Various estimation methods based on kernels, smoothing splines, local polynomials, etc. would be considered.

MSTAT 577: Analysis of Categorical Data (3, 2, 4)

This course introduces methods for analyzing response data that are categorical, rather than continuous. Topics include: categorical response data and contingency tables. Generalized linear models; Linear Models for Binary Data, Generalized Linear Models for Counts, Moments and Likelihood for Generalized Linear Models, Inference for Generalized Linear Models, Fitting Generalized Linear Models, Quasi-likelihood and Generalized Linear Models, Generalized Additive Models. Loglinear and logit models, Poisson regression, Model diagnostics, estimation procedures. Procedures in statistical packages that can handle generalized linear models will be covered.

MSTAT 579: Stochastic Processes (2, 2, 3)

Review of Probability theory, Regularity of stochastic processes, Convergence of Random walks to Brownian Motion. Brownian motion and its Martingales, Diffusion Processes, Random Time change and 1-dimensional diffusions, Brownian Motion on the half line. Convergence of Markov Chains to Diffusions, Reflected processes in Higher Dimensions Stochastic integrals, Ito’s Formula, Stochastic Differential Equations. Application in industry and finance.

MSTAT 583: Statistical Quality Control (2, 2, 3)

Development of statistical concepts and theory underlying procedures used in quality control applications. Sampling inspection procedures, the sequential probability ratio test, continuous sampling procedures, process control procedures, and experimental design. Statistical quality control demonstrates how statistics and data analysis can be applied effectively to process control and management. Topics include the definition of quality, its measurement through statistical techniques, variable and attribute control charts, CUSUM charts, multivariate control charts, process capability analysis, design of experiments, and classical and Bayesian acceptance sampling. Statistical software will be used to apply the techniques to real-life case studies from manufacturing and service industries.

MSTAT 585: Econometrics (2, 2, 3)

This course covers the. Topics include Review: mathematical expectation, Sampling distributions and inference, Regression basics. Multivariate regression: matrix form, Dummy variables and interactions; testing linear restrictions using F-tests; Inference problems - heteroscedasticity and autocorrelation. Instrumental variables and 2SLS; simultaneous equations models; measurement error. Panel Data Models, Volatility models: ARCH and GARCH family models, and multivariate volatility models. Practical using EVIEWS and R software

MSTAT 587 Non-Parametric Methods (2, 2, 3)

Topics include: Review of common smoothing techniques: Kernel estimates, nearest-neighbour estimates, spline smoothers, local polynomial estimators. Choice of smoothing parameters: Measures of estimation quality and rates of convergence, bandwidth selection by cross-validation, asymptotic distribution of kernel estimates, boundary kernels. Orthogonal series expansion and wavelets: Fourier series (some basic concepts), orthogonal series density estimates, orthogonal series regression estimates, Windowed Fourier Transform. Introduction to neural networks: From perceptron to nonlinear neuron, neural network regression, network specification. Various estimation methods based on kernels, smoothing splines, local polynomials and wavelets would be considered.

YEAR ONE: SEMESTER TWO

MSTAT 572: Advanced Sample Survey Methods (2, 2, 3)

Sample Survey Designs: Basic Concepts of Sampling, Sampling Designs: sampling with varying probabilities; Stratified, Systematic, multistage Techniques of sample design: multiphase designs; selection with probability proportional to size (PPS); Probability Sampling procedures, estimation of population total, mean and proportion. Non-probability sampling procedure, Jacknife and Bootstrap procedures for resampling. Complex Surveys. Ratio and Regression Estimations; panel design; model based sampling Survey Errors, and Re-sampling methods. Use of appropriate software to calculate standard errors (variance estimation).

MSTAT 574: Survival Analysis (2, 2, 3)

Survival distributions, Types of censored data, Estimation for various survival models, Non-parametric estimation of survival distributions, The proportional hazard and accelerated lifetime models for covariate data, Regression analysis with lifetime data. Practical Aspects; Statistical models for transfers between multiple states (e.g., alive, ill, dead), the multi-state Markov model, relationship between probabilities of transfer and transition intensities, estimation for the parameters in these models; The binomial and Poisson models of mortality.

MSTAT 576: Multivariate Analysis (2, 2, 3)

In many disciplines the basic data on an experimental unit consist of a vector of possibly correlated measurements. Examples include the chemical composition of a rock; the results of clinical observations and tests on a patient; the household expenditures on different commodities. Through the challenge of problems in a number of fields of application, this course considers appropriate statistical models for explaining the patterns of variability of such multivariate data. Topics include: Multivariate Normal distribution, Distribution of sample mean and covariance multiple, partial and canonical correlation; multivariate regression; tests on means and covariances; ANOVA; principal components analysis; factor analysis; discriminant analysis and classification; cluster analysis; multidimensional scaling.

MSTAT 578: Design and Analysis of Experiments (2, 2, 3)

An introduction to the design and analysis of experiments, Topics include the design and analysis of completely randomized designs, randomized block designs, Latin square designs, incomplete block designs, factorial designs, fractional factorial designs, nested designs and split-plot designs and response surface designs. Students will complete and present a research project on an advanced topic in experimental design. Applications involve the use of a statistical software package. Experimental Design and Analysis: Basic Concepts of Planning and Designing Experiments, Multiple Comparisons, Randomized Block Designs, Factorial Designs, Nested and Split-Plot Designs, Latin Square Designs; Analysis of Covariance and Confounding; Application, and use of Statistical Computing Packages (such SPSS, R, Genstat, Excel, etc.).

MSTAT 580: Statistical Computing and Consulting (2, 2, 3)

Consulting: Consulting introduction, Ethics, Consulting practice in industry, Student presentations about their internships, Scientific writing, Effective communication, Common issues in consulting/data analysis Case studies. Computing: Introduction to statistical computing (R–package), Least squares (regression): Penalized and weighted least squares, Density estimation and smoothing and Matrix computations. Optimization (likelihood estimation): Newton-Raphson, Fisher scoring,Combinatorial optimization. Integration (probabilities): Quadrature and Laplace approximation. Resampling and Monte Carlo inferences: Jackknife and Bootstrap, Permutation procedures and Monte Carlo simulation. Statistical graphics

MSTAT 582: Bayesian Statistics (2, 2, 3)

To introduce the concepts of Bayesian inference and the analysis of data using Bayesian methods. The concept of prior and posterior distributions; connections with the classical approach; estimation and loss; hypothesis testing and the Bayes factor; Bayesian computation and Markov Chain Monte Carlo.

MSTAT 584: Advanced Time Series Analysis (2, 2, 3)

Univariate time series: stationary, autocorrelation function, trends, ARIMA processes, unit roots, fractional ARIMA processes, forecasting, distributed lags, maximum likelihood estimation (MLE), model selection criteria, regression models with ARIMA errors and spectral analysis. Multivariate time series: Stable Vector Autoregressive (VAR) Models, Cointegration Techniques, Vector Error Correction Models (VECM), Structural VARs and VECMs, Unit Roots and Cointegration in Panels. Threshold models: TAR, STAR, ESTAR and LSTAR Models.

MSTAT 586: Spatial Statistics (2, 2, 3)

Spatial data structures: geostatistical data, lattices, and point patterns. Stationary and isotropic random fields. Autocorrelated data structures. Semivariogram estimation and spatial prediction for geostatistical data. Mapped and sampled point patterns. Regular, completely random, and clustered point processes. Spatial regression and neighborhood analyses for data on lattices.

YEAR TWO: SEMESTER ONE

MSTAT 691: Thesis I (0, 9, 9)

Seminar presentations on chosen thesis topic.

MSTAT 693: Topics in Operation Research (3, 1, 3)

Dynamic programming and heuristics. Project scheduling; probability and cost considerations in project scheduling; project control. Critical path analysis. Reliability problems, replacement and maintenance costs; discounting; group replacement, renewal process formulation, application of dynamic programming. Queuing theory in practice: obstacles in modeling queuing systems, data gathering and testing, queuing decision models, case studies. Game theory, matrix games; minimax strategies, saddle points, mixed strategies, solution of a game. Behavioural decision theory, descriptive models of human decision making; the use of decision analysis in practice.

MSTAT 695: Demographic Methods (2, 2, 3)

This course introduces the basic techniques of demographic analysis. Students will become familiar with the sources of data available for demographic research. Population composition and change measures will be presented. Measures of mortality, fertility, marriage and migration levels and patterns will be defined. Life table, standardization and population projection techniques will also be explored.

MSTAT 697 Artificial Neural Networks (2, 2, 3)

Introduction to artificial neural networks: Biological neural networks, Pattern analysis tasks: Classification, Regression, Clustering, Computational models of neurons, Structures of neural networks, Learning principles. Linear models for regression and classification: Polynomial curve fitting, Bayesian curve fitting, Linear basis function models, Bias-variance decomposition, Bayesian linear regression, Least squares for classification, Logistic regression for classification, Bayesian logistic regression for classification. Feed-forward neural networks: Pattern classification using perceptron, Multilayer feed-forward neural networks (MLFFNNs), Pattern classification and regression using MLFFNNs, Error back propagation learning, Fast learning methods: Conjugate gradient method, Auto-associative neural networks, Bayesian neural networks. Radial basis function networks: Regularization theory, RBF networks for function approximation, RBF networks for pattern classification. Kernel methods for pattern analysis: Statistical learning theory, Support vector machines for pattern classification, Support vector regression for function approximation, Relevance vector machines for classification and regression. Self-organizing maps: Pattern clustering, Topological mapping, Kohonen’s self-organizing map. Feedback neural networks: Pattern storage and retrieval, Hopfield model, Boltzmann machine, Recurrent neural networks.

YEAR TWO: SEMESTER TWO

MSTAT 692: Thesis II (0, 15, 15)

Oral examination on submitted thesis.

Programme Type

MPhil