Gibbs Sampling and Markov Chain Monte Carlo: A Modeler's Perspective

• Activity Number: 99
• Type: Other
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: ASA
• Author(s): Alan E. Gelfand*+
• Companies: Duke University
• Keywords: hierarchical models ; latent variables ; simulation

Abstract

Simulation based model fitting using Gibbs sampling and Markov chain Monte Carlo has exploded in the past twenty years and has now become a standard tool for data analysis. For many problems it provides the most practical way to implement inference. This talk will offer some historical perspective with regard to the origins of this methodology, some rudimentary features of the methodology, why its usage has exploded, and where we are today. However, the main focus of this talk will be on the phenomenal growth in the use of multi-level/hierarchical models in scientific settings and the substantial value of Markov chain Monte Carlo for the fitting of such models. We will present a brief review of the scope of settings in which hierarchical models arise. We will see that, in most cases, the hierarchical structure is built with latent variables and that these latent variables introduce unobservable process features. These features will be of interest and also facilitate model fitting. For fitting, Gibbs sampling loops become natural, updating other parameters given the values of the latent variables and then updating the latent variables given the values of the other parameters.