Nonparametric Bayes modeling of count processes

TL;DR

This paper introduces a flexible nonparametric Bayesian framework for modeling dependent count data, overcoming limitations of traditional hierarchical Poisson models by allowing for over-dispersion and complex dependencies.

Contribution

It develops a novel class of count process models based on rounding real-valued processes, with theoretical guarantees and practical algorithms for inference.

Findings

Models show good performance in simulations

Applied successfully to tumor count and asthma data

Theoretical support established for model consistency

Abstract

Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from hierarchical Poisson components. The Poisson assumption is not warranted in many applications, and hierarchical Poisson models make restrictive assumptions about over-dispersion in marginal distributions. This article proposes a class of nonparametric Bayes count process models, which are constructed through rounding real-valued underlying processes. The proposed class of models accommodates applications in which one observes separate count-valued functional data for each subject under study. Theoretical results on large support and posterior consistency are established, and computational algorithms are developed using Markov chain Monte Carlo. The methods are evaluated via simulation studies and illustrated through application to longitudinal tumor counts and asthma inhaler usage.