Spatial clustering consistency of random spanning tree partition models under infill-domain asymptotics

Music City Center 

In this research, we propose a novel blocking Bayesian spatially random spanning tree model for modeling latent spatially piecewise constant functions. We divide the spatial domain into several disjoint blocks and construct a random spanning tree model to merge blocks into spatially contiguous clusters. Under the spatial varying coefficient model setting, we provide conditions on the asymptotic rates of the number of blocks and the prior number of clusters, to obtain spatial clustering consistency results under an infill domain asymptotics. Those conditions serve as guidelines for choosing hyperparameters in our model. Based on the clustering consistency results, we also show the Bayesian posterior convergence rates of latent spatially varying coefficients and the regression mean functions.

Bayesian Posterior Concentration Theory, Infill domain asymptotics, Random Spanning Trees, Spatial Clustering