Abstract

We introduce a new model for sums of exchangeable binary random variables. The proposed distribution is an approximation to the exact distributional form, and relies on the theory of completely monotone functions and the Laplace transform of a gamma distribution function. Using Monte Carlo methods, we show that this new model compares favorably to the beta-binomial model with respect to estimating the success probability of the Bernoulli trials and the correlation between any two variables in the exchangeable set. We apply the new methodology to two classic data sets and the results are summarized.

中文翻译：

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对可交换二进制变量的总和进行建模

摘要

我们为可交换二元随机变量的总和引入了一个新模型。所提出的分布是对精确分布形式的近似，并且依赖于完全单调函数的理论和伽马分布函数的拉普拉斯变换。使用蒙特卡罗方法，我们表明，在估计伯努利试验的成功概率和可交换集合中任何两个变量之间的相关性方面，这种新模型优于 beta-二项式模型。我们将新方法应用于两个经典数据集，并对结果进行了总结。