An Introduction to Markov Chain Monte Carlo Methods
Jorge Roman, Vanderbilt University
Location: Stevenson 1307
The need to approximate an intractable integral with respect to a probability distribution P is a problem that frequently arises across many different disciplines. A popular alternative to numerical integration and analytical approximation methods is the Monte Carlo (MC) method which uses computer simulations to estimate the integral. In the MC method, one generates independent and identically distributed (iid) samples from P and then uses sample averages to estimate the integral. However, in many situations, P is a complex high-dimensional probability distribution and obtaining iid samples from it is either impossible or impractical. When this happens, one may still be able to use the increasingly popular Markov chain Monte Carlo (MCMC) method in which the iid draws are replaced by a Markov chain that has P as its stationary distribution. In this talk, I will give a brief introduction to the MC and MCMC methods. The focus will be on the MCMC method and its applications to Bayesian statistics.