Fast Bayesian Inference for Spatial Mean-Parameterized Conway-Maxwell-Poisson Models

Area of Science:

• Statistics
• Biostatistics
• Spatial Analysis

Background:

• Count data frequently exhibit zero inflation, spatial dependence, and non-equidispersion across various scientific fields.
• Existing models like the Conway-Maxwell-Poisson (COMP) and generalized Poisson distributions have limitations regarding parameter constraints and interpretability.
• There is a need for flexible and interpretable models to analyze complex count data with spatial structures.

Purpose of the Study:

• To propose novel spatial mean-parameterized COMP models that address the interpretability and parameter space challenges of existing methods.
• To develop an efficient Bayesian spatial filtering approach for high-dimensional spatial count data.
• To introduce a fast computational strategy for the COMP distribution, tackling its intractable likelihood and non-closed-form mean.

Main Methods:

• Development of spatial mean-parameterized Conway-Maxwell-Poisson (COMP) models.
• Application of Bayesian spatial filtering with reversible-jump Markov chain Monte Carlo (MCMC) for automatic basis vector selection.
• Implementation of an auxiliary variable algorithm and pre-computed approximations for efficient COMP likelihood evaluation.

Main Results:

• The proposed models successfully retain the flexibility of existing methods while resolving issues with parameter interpretability and constraints.
• The Bayesian spatial filtering approach efficiently handles high-dimensional spatial data.
• The computational methods significantly improve the speed and feasibility of analyzing COMP distributions.

Conclusions:

• Spatial mean-parameterized COMP models offer a flexible, interpretable, and computationally efficient solution for complex count data with spatial dependence.
• The methodology is broadly applicable to various disciplines, including public health and ecology, as demonstrated with real-world datasets.
• The developed computational techniques enhance the practical utility of COMP models in statistical analysis.