The Poisson compound decision problem is a classical problem in statistics, for which parametric and nonparametric empirical Bayes methodologies are available to estimate the Poisson's means in static or batch domains. In this paper, we consider the Poisson compound decision problem in a streaming or online domain. By relying on a quasi-Bayesian approach, often referred to as Newton's algorithm, we obtain sequential Poisson's mean estimates that are of easy evaluation, computationally efficient and with a constant computational cost as data increase, which is desirable for streaming data. Large sample asymptotic properties of the proposed estimates are investigated, also providing frequentist guarantees in terms of a regret analysis. We validate empirically our methodology, both on synthetic and real data, comparing against the most popular alternatives.

翻译：泊松复合决策问题是统计学中的经典问题，针对静态或批处理领域已有参数化和非参数化经验贝叶斯方法可用于估计泊松均值。本文研究流式或在线领域中的泊松复合决策问题。通过采用常被称为牛顿算法的准贝叶斯方法，我们获得了易于评估、计算高效且计算成本随数据增长保持恒定的序贯泊松均值估计量，这对流式数据具有显著优势。本文研究了所提估计量的大样本渐近性质，并通过遗憾分析提供了频率学保证。我们在合成数据与真实数据上对所提方法进行了实证验证，并与主流替代方法进行了比较。