Abstract
Spatial data are very often heterogeneous, which indicates that there may not be a unique simple statistical model describing the data. To overcome this issue, the data can be segmented into a number of homogeneous regions (or domains). Identifying these domains is one of the important problems in spatial data analysis. Spatial segmentation is used in many different fields including epidemiology, criminology, ecology, and economics. To solve this clustering problem, we propose to use the change-point methodology. In this paper, we develop a new spatial segmentation algorithm within the framework of the generalized Gibbs sampler. We estimate the average surface profile of binary spatial data observed over a two-dimensional regular lattice. We illustrate the performance of the proposed algorithm with examples using artificially generated and real data sets.
Highlights
Our study aims to develop effective procedures based on an Markov chain Monte Carlo (MCMC) algorithm within the generalized Gibbs sampler (GGS) framework for estimating the average surface profile explaining the heterogeneity of the data
We compare the proposed GGS algorithm to the Sequential Importance Sampling (SIS) algorithm, which is previously developed for the same type of spatial segmentation problem [31]
Both SIS and GGS algorithms aim at the same posterior distribution but they are different in their nature
Summary
The objective of our study, which is motivated by analysis of the distribution of plant species, is to identify homogeneous domains in binary spatial data observed over a two-dimensional regular lattice This model belongs to the class of autologistic models introduced by Besag [16]. Parameter estimation or drawing samples from posterior distribution for this model is a notoriously difficult problem due to the complex form of likelihood function.The alternative methods to maximum likelihood estimate include pseudolikelihood and Monte Carlo maximum likelihood estimators [17,18] To analyse this model within the Bayesian framework, a significant step was made by Moller [19], who proposed an auxiliary variable MCMC method that draws independent samples from unnormalised density by constructing the proposal distribution that cancels the normalising constant from Metropolis-Hastings ratio.
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