标题： 一个贝叶斯非参数卡方拟合优度检验 显示英文标题

标题： A Bayesian nonparametric chi-squared goodness-of-fit test

摘要： 贝叶斯非参数推断和 Dirichlet 过程是统计方法中的流行工具。 本文中，我们在假设检验中使用 Dirichlet 过程提出了一个贝叶斯非参数卡方拟合优度检验。 在我们的贝叶斯非参数方法中，我们将 Dirichlet 过程视为数据分布的先验，并基于更新后的 Dirichlet 过程与假设分布 F0 之间的 Kullback-Leibler 距离来进行检验。 我们证明了此距离渐近收敛到与卡方检验相同的卡方分布。 类似地，为列联表提供了贝叶斯非参数独立性卡方检验。 此外，通过计算 Dirichlet 过程与假设分布之间的 Kullback-Leibler 距离，提出了一种获得 Dirichlet 过程适当集中参数的方法。 显示英文摘要

摘要： The Bayesian nonparametric inference and Dirichlet process are popular tools in statistical methodologies. In this paper, we employ the Dirichlet process in hypothesis testing to propose a Bayesian nonparametric chi-squared goodness-of-fit test. In our Bayesian nonparametric approach, we consider the Dirichlet process as the prior for the distribution of data and carry out the test based on the Kullback-Leibler distance between the updated Dirichlet process and the hypothesized distribution F0. We prove that this distance asymptotically converges to the same chi-squared distribution as the chi-squared test does. Similarly, a Bayesian nonparametric chi-squared test of independence for a contingency table is provided. Also, by computing the Kullback-Leibler distance between the Dirichlet process and the hypothesized distribution, a method to obtain an appropriate concentration parameter for the Dirichlet process is suggested.