Autologistic Models for Binary Data on a Lattice

• Activity Number: 249
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): John Hughes*+ and Murali Haran and Petrutza Caragea
• Companies: Penn State and Penn State and Iowa State University
• Keywords: Markov random field ; pseudolikelihood ; maximum likelihood ; Bayesian ; perfect sampling ; parallel computation

Abstract

The autologistic model is a Markov random field model for binary data on a lattice. We consider inference and computation for two models: the original autologistic model due to Besag, and the centered autologistic model proposed recently by Caragea and Kaiser. We study pseudolikelihood (PL), maximum likelihood, and Bayesian approaches to inference and describe ways to optimize the efficiency of these algorithms and the perfect sampling algorithms upon which they depend. We conduct a thorough simulation study and find that inference for regression parameters in the centered model is reliable only for large lattices and no more than moderate spatial dependence. When the lattice is large enough, and the dependence small enough, to permit reliable inference, the three approaches perform comparably, and so we recommend the PL approach for its easier implementation and much faster execution.