Fast Bayesian inference for spatial mean-parameterized Conway-Maxwell-Poisson models

TL;DR

This paper introduces a fast Bayesian spatial mean-parameterized Conway-Maxwell-Poisson model that effectively handles complex count data features like zero inflation and spatial dependence, with efficient computation and automatic basis selection.

Contribution

It proposes a novel spatial mean-parameterized COMP model with a Bayesian spatial filtering approach and reversible-jump MCMC, addressing computational challenges and interpretability issues.

Findings

Efficient auxiliary variable algorithm for likelihood evaluation

Automatic basis vector selection via reversible-jump MCMC

Successful application to real datasets including HPV-cancer and vaccine refusal

Abstract

Count data with complex features arise in many disciplines, including ecology, agriculture, criminology, medicine, and public health. Zero inflation, spatial dependence, and non-equidispersion are common features in count data. There are two classes of models that allow for these features -- he mode-parameterized Conway--Maxwell--Poisson (COMP) distribution and the generalized Poisson model. However both require the use of either constraints on the parameter space or a parameterization that leads to challenges in interpretability. We propose a spatial mean-parameterized COMP model that retains the flexibility of these models while resolving the above issues. We use a Bayesian spatial filtering approach in order to efficiently handle high-dimensional spatial data and we use reversible-jump MCMC to automatically choose the basis vectors for spatial filtering. The COMP distribution poses two additional computational challenges -- an intractable normalizing function in the likelihood and no closed-form expression for the mean. We propose a fast computational approach that addresses these challenges by, respectively, introducing an efficient auxiliary variable algorithm and pre-computing key approximations for fast likelihood evaluation. We illustrate the application of our methodology to simulated and real datasets, including Texas HPV-cancer data and US vaccine refusal data.