Journal Article

Partially Collapsed Gibbs Samplers

Park, Taeyoung, van Dyk, David A

2008

Overview

Ever-increasing computational power, along with ever-more sophisticated statistical computing techniques, is making it possible to fit ever-more complex statistical models. Among the more computationally intensive methods, the Gibbs sampler is popular because of its simplicity and power to effectively generate samples from a high-dimensional probability distribution. Despite its simple implementation and description, however, the Gibbs sampler is criticized for its sometimes slow convergence, especially when it is used to fit highly structured complex models. Here we present partially collapsed Gibbs sampling strategies that improve the convergence by capitalizing on a set of functionally incompatible conditional distributions. Such incompatibility generally is avoided in the construction of a Gibbs sampler, because the resulting convergence properties are not well understood. We introduce three basic tools (marginalization, permutation, and trimming) that allow us to transform a Gibbs sampler into a partially collapsed Gibbs sampler with known stationary distribution and faster convergence.

• Publisher: Taylor & Francis,American Statistical Association,Taylor & Francis Ltd
• Subject: Applications / Autocorrelation / Blocking / Computational methods / Conditional convergence / Convergence / Correlations / Data sampling / Distribution theory / Estimation / Exact sciences and technology / General topics / Gibbs sampler / Incompatible Gibbs sampler / Index sets / Marginal data augmentation / Marginality / Marginalization / Markov chains / Mathematics / Power / Probability / Probability and statistics / Probability theory and stochastic processes / Property / Random sampling / Rate of convergence / Sampling / Sampling distributions / Sampling techniques / Sampling theory, sample surveys / Sciences and techniques of general use / Simplicity / Statistical methods / Statistical models / Statistical variance / Statistics / Theory and Methods