Robust Bayesian Modeling of Counts with Zero inflation and Outliers: Theoretical Robustness and Efficient Computation

TL;DR

This paper proposes a robust Bayesian framework for count data that effectively handles zero inflation and outliers, ensuring computational efficiency and theoretical robustness, with applications in trend filtering and spatial modeling.

Contribution

It introduces a rescaled beta distribution for robust Bayesian count modeling, providing a computationally efficient Gibbs sampler and guaranteed robustness against outliers.

Findings

The method automatically removes extreme outliers from the posterior.

It achieves efficient computation through a custom Gibbs sampling algorithm.

The approach is validated in trend filtering and spatial modeling applications.

Abstract

Count data with zero inflation and large outliers are ubiquitous in many scientific applications. However, posterior analysis under a standard statistical model, such as Poisson or negative binomial distribution, is sensitive to such contamination. This study introduces a novel framework for Bayesian modeling of counts that is robust to both zero inflation and large outliers. In doing so, we introduce rescaled beta distribution and adopt it to absorb undesirable effects from zero and outlying counts. The proposed approach has two appealing features: the efficiency of the posterior computation via a custom Gibbs sampling algorithm and a theoretically guaranteed posterior robustness, where extreme outliers are automatically removed from the posterior distribution. We demonstrate the usefulness of the proposed method by applying it to trend filtering and spatial modeling using predictive Gaussian processes.