A transdimensional MCMC sampler for spatially dependent mixture models

We consider the problem of spatially dependent areal data, where for each area independent observations are available, and propose to model the density of each area through a finite mixture of Gaussian distributions. The spatial dependence is introduced via a novel joint distribution for a collection of vectors in the simplex, that we term logisticMCAR. We also discuss a generalization of the mixture model with a random number of components, introducing a reversible jump algorithm to sample from the full posterior. Through simulated data examples we check the performance of our algorithm. Moreover, we present an application on a real dataset of Airbnb listings in the city of Amsterdam, also showing how to easily incorporate for additional covariate information in the model.