Modeling sparse count data, which arise across numerous scientific fields, presents significant statistical challenges. This chapter addresses these challenges in the context of infectious disease prediction, with a focus on predicting outbreaks in geographic regions that have historically reported zero cases. To this end, we present the detailed computational framework and experimental application of the Poisson Hierarchical Indian Buffet Process (PHIBP), with demonstrated success in handling sparse count data in microbiome and ecological studies. The PHIBP's architecture, grounded in the concept of absolute abundance, systematically borrows statistical strength from related regions and circumvents the known sensitivities of relative-rate methods to zero counts. Through a series of experiments on infectious disease data, we show that this principled approach provides a robust foundation for generating coherent predictive distributions and for the effective use of comparative measures such as alpha and beta diversity. The chapter's emphasis on algorithmic implementation and experimental results confirms that this unified framework delivers both accurate outbreak predictions and meaningful epidemiological insights in data-sparse settings.

翻译：稀疏计数数据广泛存在于众多科学领域，其建模带来了显著的统计学挑战。本章在传染病预测的背景下探讨这些挑战，重点关注在历史上报告零病例的地理区域进行疫情预测。为此，我们详细阐述了泊松分层印度自助餐过程（PHIBP）的计算框架与实验应用，该方法已在微生物组和生态学研究中被证实能成功处理稀疏计数数据。PHIBP架构基于绝对丰度概念，系统性地从相关区域借用统计强度，并规避了相对比率方法对零计数的已知敏感性。通过对传染病数据的一系列实验，我们证明这一原则性方法为生成一致的预测分布以及有效运用α与β多样性等比较度量提供了稳健基础。本章对算法实现和实验结果的强调证实，这一统一框架能在数据稀疏环境下同时提供准确的疫情预测和有意义的流行病学见解。