A Bayesian nonparametric model for spatial clustering

Spatial areal data often exhibit dependence among neighbouring regions, making independence assumptions unrealistic. Hierarchical Bayesian models incorporate spatial structure to improve estimation stability. Gaussian Markov random fields are commonly used but may oversmooth spatial surfaces due to quadratic regularization. To better capture spatial heterogeneity and sharp boundaries, we propose a nonparametric clustering model based on a Dirichlet process mixture with a Markov random field prior on cluster allocations. The number of clusters is inferred from the data while neighbouring areas are encouraged to share cluster membership. Posterior inference is carried out via an MCMC algorithm using a double Metropolis–Hastings scheme to handle an intractable normalizing constant. The proposed approach is illustrated using Italian Autism Spectrum Disorder data.