Markov Chain Monte Carlo (MCMC) methods are now used extensively in both frequentist and Bayesian statistics. MCMC is most commonly used to obtain estimates of summary statistics, model parameters, and their standard errors (posterior variances). In some situations, MCMC estimates are known to have more desirable statistical properties than those obtained with other methods, such as moments and Iterative Generalised Least Squares. For example, when fitting multilevel logistic models. However the application of MCMC methods requires some careful consideration; especially in deciding the starting values for the process and assessing when the estimates have converged. 

As well as providing a theoretical background, there will also be practical sessions including setting up MCMC estimation in R, using MCMC estimation in statistical modelling and small area estimation.

Course Objectives

On this two day course, we will:

• explain the basic idea of MCMC

• show in depth how MCMC estimates are generated

• give some examples of the application of MCMC in Mathematical and Social Statistics, including multilevel modelling, and small area estimation.

• compare the pros and cons of MCMC with other estimation techniques.

Target Audience

Social Scientists with some quantitative background or Mathematical Statisticians with an interest in how MCMC estimation methods work for situations such as getting estimates of model parameters.

Preliminary Reading

• D. Gamerman (1997) Markov Chain Monte Carlo: Stochastic Simulation of Bayesian Inference (Chapman & Hall Texts in Statistical Science) .