Page 40 - Handbook PG 20182019

Faculty of Science Postgraduate Booklet, Session 2018/2019

SQB7008 STOCHASTIC MODELS

Poisson processes, backward and forward Kolmogorov equations, birth and death processes and
examples. Definition and concepts in renewal processes, distribution for the number of renewal,
renewal function and theorems for renewal processes.

Backward and forward renewal times. Examples for various types of renewal processes. Examples of
applications of the theory in renewal processes.

Assessment Methods:
Continuous Assessment 50%
Final Examination 50%

Medium of Instruction:
English

Transferable Skills:
-

Humanity Skill:
CT5, TS5, LS4

References:
1. Cox, D. R. and Miller, H. D. (1965). The Theory of Stochastic Processes. Chapman & Hall.
2. Durret, R. (2012). Essential of Stochastic Process (electronic resource). Springer.
3. Cox, D. R. (1962). Renewal Theory, Methuen.
4. Taylor, H. M. and Karlin, S. (1994). An Introduction to Stochastic Modelling. Academic Press.

SQB7009 Bayesian Statistics

Different functions relevant to Bayesian statistics, calculation of E (x) and Var (x). Hypothesis testing
of proportion, mean for posterior distribution, choice of sample size. Sufficient statistics and
efficiency. Bayesian estimators and properties of estimators. Loss function, Bayesian risk. Decision
2
theory on x , subjective information compared to objective information. Bayesian decision criterion.
Expected opportunity loss (EOL). Bayesian inference - Beta-Binomial, Uniform prior, Beta prior,
conjugate family, Jeffrey’s prior. Choosing the prior Beta-Binomial - with vague prior, with conjugate
prior information, choosing prior when you have real prior knowledge, constructing a general
continuous prior, effect of prior. Bayes’ theorem for Normal mean with discrete and continuous
prior. Flat prior density (Jeffrey’s prior) for Normal mean.

Assessment Methods:
Continuous Assessment 50%
Final Examination 50%

Medium of Instruction:
English

Transferable Skills:
-

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