Graduate Seminar

Chris Potter
Carnegie Mellon University
Title: No More .234: Realistic Optimization of Monte Carlo Methods

Abstract: With the explosion of computing power in recent times, many scientists and engineers have turned to computer simulation as a tool in solving problems that but a few decades ago were considered unsolvable. Sampling from complicated probability distributions is a crucial requirement of the most interesting simulations, and the most common tools for this task come from the Markov Chain Monte Carlo (MCMC) family of samplers. Fortunately or unfortunately, these samplers come with a lot of parameters to tune, and a poorly tuned MCMC sampler can be extremely inefficient when employed to tackle a large simulation.

Hundreds of non-mathematicians seeking a simple way to produce efficient MCMC have latched on to a 1996 paper by Gelman, Roberts, and Gilks (GRG), which claims that setting the most fundamental MCMC parameter (the acceptance ratio) to .234 produces optimal efficiency for all sufficiently large MCMC samplers which satisfy a small number of hypotheses.

GRG's proof relying on an SDE-based view of MCMC is rigorous and correct, but as usual the devil is in the hypotheses. After a gentle introduction to MCMC theory, we will see that the relevance of GRG's claim to practical computations is actually quite limited, and explore some interesting and possibly counterintuitive discoveries made along the way to confirming this fact.

Date: Tuesday, October 30, 2012
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Brian Kell