STA3043S - Statistical Modelling, Machine Learning & Bayesian

Course Outline:

This course forms part of the third-year major in Mathematical Statistics. It consists of three modules: The first, Generalised Linear Models, introduces students to the theory and application of fitting linear models to various types of response variables with different underlying distributions. Subsequently, elementary concepts and methods in machine learning within the framework of statistical learning are explored. Finally, the Introduction to Bayesian Analysis module is dedicated to the Bayesian paradigm of statistical inference, analysis, and risk theory. The contents of the respective modules are outlined as follows: Generalized linear models: Topics covered include: The exponential family of distributions, the GLM formulation, estimation and inference, models for continuous responses with skew distributions, logistic regression, log-linear models and Poisson regression. Machine learning: Topics covered include: A basic introduction to statistical learning paradigms, applications of regression and classification trees, and a primer on feedforward neural networks and backpropagation. Introduction to Bayesian Analysis: Topics covered include: use of Bayes’ theorem; Bayesian statistical analysis for Bernoulli and normal sampling; empirical Bayes and credibility theory; loss and extreme value distributions; Monte Carlo methods. Students are assessed through formal written exam plus computer assignments done under exam conditions.