Monte Carlo methods for spatial clustering

Spatial clustering is an important component of spatial data analysis because of a possible heterogeneity of the data. Ignoring the spatial segmentation may lead to incorrect interpretation of parameters in the corresponding statistical model while spatial clustering allows us to develop an appropriate statistical model for each homogeneous domain. The problem of nding regional homogeneous domains is known as segmentation, partitioning or clustering which is commonly used in disease surveillance, spatial epidemiology, population genetics, landscape ecology, crime analysis and many other elds. For example, in epidemiology and public health, it is known that the disease risk varies across space and it is important to identify regions of safety and regions of risks. In this study, we focus on identifying homogeneous domains in binary data, which indicate the presence or absence of a certain plant species which are observed over a two-dimensional lattice. We consider this clustering problem within the change-point detection methodology. We developed a sequential importance sampling algorithm to estimate the average surface prole explaining the hetrogeneity of data [1]. We provide numerical experiments, which illustrate the eectiveness of this method and compare with the results obtained via MCMC algorithm within the generalized Gibbs sampler.