Modeling spatial-temporal binary data using Markov random fields |
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Authors: | Email author" target="_blank">Jun?ZhuEmail author Hsin-Cheng?Huang Jungpin?Wu |
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Institution: | 1.Department of Statistics,University of Wisconsin-Madison,Madison;2.Institute of Statistical,Science Academia Sinica,Taipei,Taiwan;3.Department of Statistics,Feng Chia University,Taichung,Taiwan |
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Abstract: | An autologistic regression model consists of a logistic regression of a response variable on explanatory variables and an
autoregression on responses at neighboring locations on a lattice. It is a Markov random field with pairwise spatial dependence
and is a popular tool for modeling spatial binary responses. In this article, we add a temporal component to the autologistic
regression model for spatial-temporal binary data. The spatial-temporal autologistic regression model captures the relationship
between a binary response and potential explanatory variables, and adjusts for both spatial dependence and temporal dependence
simultaneously by a space-time Markov random field. We estimate the model parameters by maximum pseudo-likelihood and obtain
optimal prediction of future responses on the lattice by a Gibbs sampler. For illustration, the method is applied to study
the outbreaks of southern pine bettle in North Carolina. We also discuss the generality of our approach for modeling other
types of spatial-temporal lattice data. |
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Keywords: | |
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