# Nonparametric Bayes modeling of count processes

arXiv: https://arxiv.org/abs/1307.2822 · HTML: https://mlsanity.com/paper/1307.2822/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2013.

## Built on by (most cited first, 3 of 3)

- [Semiparametric count data regression for self-reported mental health](https://mlsanity.com/paper/2106.09114/) (2021)
- [Semiparametric discrete data regression with Monte Carlo inference and prediction](https://mlsanity.com/paper/2110.12316/) (2021)
- [Warped Dynamic Linear Models for Time Series of Counts](https://mlsanity.com/paper/2110.14790/) (2021)

## Abstract (arXiv)

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.