Abstract: Understanding the heterogeneity over spatial locations is an important problem that has been widely studied in applications such as economics and environmental science. We focus on regression models for spatial panel data analyses, where repeated measurements are collected over time at various spatial locations. We propose a novel class of nonparametric priors that combines a Markov random field (MRF) with the product partition model (PPM), and show that the resulting prior, called MRF-PPM, is capable of identifying latent group structures among the spatial locations, while efficiently using the spatial dependence information. We derive a closed-form conditional distribution for the proposed prior and introduce a new way of computing the marginal likelihood that renders an efficient Bayesian inference. Furthermore, we study the theoretical properties of the proposed MRF-PPM prior and show a clustering consistency result for the posterior distribution. We demonstrate the excellent empirical performance of our method using extensive simulation studies and applications to US precipitation data and a California median household income data study.

Key words and phrases: Marginal likelihood, nonparametric Bayesian method, posterior consistency, spatial homogeneity.