Advances in MCMC for Spatial Generalized Linear Mixed Models

• Activity Number: 223
• Type: Topic Contributed
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): John Hughes*+
• Companies: University of Minnesota
• Keywords: generalized linear model ; spatial ; mixed model ; MCMC ; regression ; statistical computing

Abstract

Non-Gaussian areal data are common in many fields, e.g., epidemiology, marketing, agriculture, ecology, forestry, geography, and image analysis. The spatial generalized linear mixed model (SGLMM) offers a very popular and flexible approach to modeling such data, but the traditional SGLMM suffers from two major shortcomings: (1) variance inflation due to spatial confounding, and (2) high-dimensional spatial random effects that make fully Bayesian inference for such models computationally challenging. Univariate updating of the random effects results in a slow-mixing Markov chain because the random effects are strongly correlated. This has led to a number of approaches that involve updating the random effects in a block(s). Constructing proposals for these updates is challenging, and the improved mixing comes at the cost of increased running time per iteration. We will discuss recent reparameterizations of the SGLMM that alleviate spatial confounding and permit the random effects to be handled so efficiently that even the largest areal datasets can be analyzed quickly.