MCMC Sampling Geospatial Partitions for Linear Models

Geospatial statistical approaches must frequently confront the problem of correctlypartitioning a group of geographical sub-units, such as counties, states, or precincts,into larger blocks which share information. Since the space of potential partitions isquite large, sophisticated approaches are required, particularly when this partitioninginteracts with other parts of a larger model, as is frequent with Bayesian inference.Authors such as Balocchi et al. (2021) provide stochastic search algorithms whichprovide certain theoretical guarantees about this partition in the context of Bayesianmodel averaging. We borrow tools from Herschlag et al. (2020) to examine a potentialapproach to sampling these clusters efficiently using a Markov Chain Monte Carlo(MCMC) approach.