  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.
