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.

翻译：在许多科学应用中，具有零膨胀和大异常值的计数数据普遍存在。然而，在标准统计模型（如泊松或负二项分布）下进行后验分析时，极易受到此类污染的影响。本研究提出了一种新颖的贝叶斯计数建模框架，对零膨胀和大异常值均具有鲁棒性。为此，我们引入了重缩放Beta分布，并利用其吸收零值及异常计数产生的不良效应。该方法具有两大优势：一是通过定制吉布斯采样算法实现后验计算的高效性；二是后验鲁棒性具有理论保障，即极端异常值会自动从后验分布中剔除。我们通过将所提方法应用于基于预测高斯过程的趋势滤波与空间建模，验证了其实用价值。