Spatial Product Partition Models

Abstract

When modeling geostatistical or areal data, spatial structure is commonly accommodated via a covariance function for the former and a neighborhood structure for the latter. In both cases the resulting spatial structure is a consequence of implicit spatial grouping in that observations near in space are assumed to behave similarly. It would be desirable to develop spatial methods that explicitly model the partitioning of spatial locations providing more control over resulting spatial structures and be able to better balance local and global spatial dependence. To this end, we extend product partition models to a spatial setting so that the partitioning of locations into spatially dependent clusters is explicitly modeled. We explore the resulting spatial structure and demonstrate its flexibility in accommodating many types of spatial dependencies. We illustrate the method’s utility through simulation studies and two applications. Computational techniques with additional simulations are provided in a Supplementary Material file available online.