ABSTRACT
ABSTRACT The problem of modeling and analyzing point referenced binary spatial data is addressed. We formulate a hierarchical model introducing spatial effects at the second stage. Rather than capturing the second stage spatial association using a Markov random field specification, we employ a second order stationary Gaussian spatial process. In fact, we introduce a convenient latent Gaussian spatial process making our observed data a realization of an indicator process on this latent process. Convenient analytic results ensue. Working with a Gaussian process specification introduces the need for matrix inversion to implement likelihood or Bayesian inference. When the number of sites is large, high dimensional inversion is required which is slow (or possibly infeasible) and subject to inaccuracy and instability. We propose an alternative approach replacing inversion with simulation by introducing a suitable importance sampling density. We illustrate with the analysis of a set of repeat sales of residential properties in Baton Rouge, Louisiana.
