A Bayesian nonparametric model for count functional data

Count functional data arise in a variety of applications, including longitudinal, spatial and imaging studies measuring functional count responses for each subject under study. 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 discuss a class of nonparametric Bayes count functional data models introduced in Canale and Dunson (2012), which are constructed through rounding real-valued underlying processes. Computational algorithms are developed using Markov chain Monte Carlo and the methods are illustrated through application to asthma inhaler usage.