Statistics
ST417: Introduction to Bayesian Modelling (5 ECTS)
An introductory course to Bayesian statistical modelling and analysis. Covers basic theory and methods of Bayesian model development and focuses on inference which is based on simulations (computations done in R). A prerequisite is a calculus based course in probability (at the level of MA235, for example). Prior experience studying statistics or regression analysis is helpful but not necessary.
Taught in Semester(s) II. Examined in Semester(s) II.
Workload: 28 hours (24 Lecture hours, 4 Tutorial hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Determine likelihood and prior distributions as parts of a basic Bayesian model specification.
- Apply Bayes theorem to obtain posterior distribution of unknown random variables in the model.
- Derive posterior predictive distribution.
- Write simple R scripts implementing basic random sampling methods.
- Apply the basics of Markov chain theory to implement simulation algorithms for inference.
- Implement Gibbs sampler and Metropolis algorithm to obtain samples from posterior distributions.
- Compare and contrast basic Bayesian methods with classical statistics and realize advanatges and disadvantages of both.
- Develop simple Bayesian models for analysis of real world data sets.
Indicative Content
The goal of this course is to introduce the main ideas and methods of Bayesian inference to develop fully probabilistic models for statistical analysis. It covers the basic methods of Bayesian model development, including specification of prior distributions and likelihood, their combining through Bayes theorem, and conducting the inference about unknown random variables in the model. The inference is based on simulations (computations done in R) which produce posterior and predictive distributions. Simulations implement basic sampling techniques such as Gibbs sampler and Metropolis algorithm.
Module Resources
- William Bolstad, Introduction to Bayesian Statistics, Wiley (2007).
- Peter Hoff, A First Course in Bayesian Statistical Methods, Springer (2009).
- Gelman, Carlin, Stern and Rubin, Bayesian Data Analysis, Chapman & Hall / CRC (2004).
- Michael Lavine, Introduction to Statistical Thought NOTE: Available online: http://www.math.umass.edu/~lavine/Book/book.html
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