Generalized Direct Sampling for Large-Scale Hierarchical Bayesian Models

• Activity Number: 119
• Type: Topic Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Michael Braun*+ and Paul Damien
• Companies: Massachusetts Institute of Technology and The University of Texas at Austin
• Keywords: Parallel computing ; Simulation ; Direct Sampling ; Hierarchical Models

Abstract

Generalized Direct Sampling (GDS) is an estimation method for hierarchical Bayesian models that generates samples from a multidimensional posterior distribution. Like the Direct Sampling (DS) algorithm of Walker, et.al., but unlike MCMC, GDS samples are independent, so they can collected in parallel (taking advantage of computers with multiple processing cores), without concerns about autocorrelation and chain convergence. But unlike DS, GDS separates the estimation method from the model specification, so the efficiency of the sampler does not depend directly on the choice of the prior. Also, GDS resolves a numerical stability problem of DS that makes GDS more useful for large-scale hierarchical models with many thousands of parameters. Consequently, GDS has the potential to replace MCMC as the preferred estimation method for a broadly general class of Bayesian models, and can be a frequently used addition to the statistician's toolbox.