Author Information

Jonathan M. Graham

Abstract

With exponential family models for dependent data, such as the autologistic model for binary spatial lattice data, maximum likelihood estimates can be obtained using Markov chain sampling methods by simulating an ergodic Markov chain which converges weakly to the equilibrium distribution of the model. This Markov chain Monte Carlo maximum likelihood (MCMCML) procedure provides a competitor to the usual pseudolikelihood estimation method often used for modeling discrete lattice data. Within this MCMCML framework, it is also possible to conduct formal inference using MCMC analogues to the usual likelihood ratio, Wald, and Lagrange multiplier tests, for which the asymptotic distributions are known subject to some mild regularity conditions. Here, the MCMC methodology will be discussed as it pertains to the autologistic model for binary data and will be used to model the spatial pattern of disease spread in bell pepper caused by the pathogen Phytophthora capsici.

Keywords

Autologistic model, Markov chain Monte Carlo (MCMC)

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Apr 28th, 11:30 AM

MARKOV CHAIN MONTE CARLO METHODS FOR MODELING THE SPATIAL PATTERN OF DISEASE SPREAD IN BELL PEPPER

With exponential family models for dependent data, such as the autologistic model for binary spatial lattice data, maximum likelihood estimates can be obtained using Markov chain sampling methods by simulating an ergodic Markov chain which converges weakly to the equilibrium distribution of the model. This Markov chain Monte Carlo maximum likelihood (MCMCML) procedure provides a competitor to the usual pseudolikelihood estimation method often used for modeling discrete lattice data. Within this MCMCML framework, it is also possible to conduct formal inference using MCMC analogues to the usual likelihood ratio, Wald, and Lagrange multiplier tests, for which the asymptotic distributions are known subject to some mild regularity conditions. Here, the MCMC methodology will be discussed as it pertains to the autologistic model for binary data and will be used to model the spatial pattern of disease spread in bell pepper caused by the pathogen Phytophthora capsici.