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<p>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. </p>
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