MATH48122 - 2010/2011

 

Specification

Aims

To introduce the student to computational Bayesian statistics, in particular Markov chain Monte Carlo (MCMC)

Brief Description of the unit

Since the late 1980's MCMC has been widely used in statistics and the range of its applications are ever increasing. This course will introduce MCMC methodology, in particular, the Metropolis-Hastings algorithm which is the basis for all MCMC. The implementation of MCMC will be discussed in detail with numerous examples.

Learning Outcomes

On successful completion of this course unit students will be able to

• apply the Metropolis-Hastings algorithm and Gibbs sampler to standard problems;
• understand the issues involved with the implementation of MCMC;
• appreciate how computers can assist with Bayesian statistics.

Future topics requiring this course unit

None.

Syllabus

1. Introduction: Bayesian statistics, Markov chains. [2]
2. Gibbs Sampler: data augmentation, burn-in, convergence. [4]
3. Metropolis-Hastings algorithm: independent sampler, random walk Metropolis, scaling, multi-modality. [4]
4. MCMC Issues: Monte Carlo Error, reparameterisation, hybrid algorithms, convergence diagnostics. [4]
5. Perfect Simulation and adaptive MCMC. [3]
6. Reversible jump MCMC: unknown number of parameters. [3]
7. Approximate Bayesian Computation: simulation based inference. [2]

Textbooks

• W. R. Gilks, S. Richarson and D. Spiegelhalter, Markov chain Monte Carlo methods in Practice, Chapman and Hall.

Teaching and learning methods

Two lectures plus two hour computer workshop each week. In addition students should expect to spend at least 6 hours each week on private study for this course unit.

Assessment

Weekly courseworks: 50%

End of semester written examination: two hours 50%

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Arrangements