Spatially dependent mixture models via the Logistic Multivariate CAR prior

TL;DR

This paper introduces a novel spatially dependent mixture model called logisticMCAR for areal data, enabling better density estimation across disconnected regions with different features, demonstrated through real-world Airbnb data.

Contribution

The paper proposes the logisticMCAR prior for modeling spatial dependence in mixture models, with an efficient MCMC algorithm and demonstrated advantages over existing methods.

Findings

Better density estimation in disconnected areas.

Effective incorporation of covariate information.

Validated on Airbnb data in Amsterdam.

Abstract

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 show that salient features of the logisticMCAR distribution can be described analytically, and that a suitable augmentation scheme based on the P\'olya-Gamma identity allows to derive an efficient Markov Chain Monte Carlo algorithm. When compared to competitors, our model has proved to better estimate densities in different (disconnected) areal locations when they have different characteristics. We discuss 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.