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Goodness-of-fit tests based on the distance between the Dirichlet process and its base measure

机译:基于Dirichlet过程与其基本度量之间的距离的拟合优度检验

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摘要

The Dirichlet process is a fundamental tool in studying Bayesian nonparametric inference. The Dirichlet process has several sum representations, where each one of these representations highlights some aspects of this important process. In this paper, we use the sum representations of the Dirichlet process to derive explicit expressions that are used to calculate Kolmogorov, Levy, and Cramer-von Mises distances between the Dirichlet process and its base measure. The derived expressions of the distance are used to select a proper value for the concentration parameter of the Dirichlet process. These tools are also used in a goodness-of-fit test. Illustrative examples and simulation results are included.
机译:Dirichlet过程是研究贝叶斯非参数推断的基本工具。 Dirichlet过程具有多个总和表示,其中每个表示都突出了此重要过程的某些方面。在本文中,我们使用Dirichlet过程的和表示来导出显式,这些显式用于计算Dirichlet过程与其基本度量之间的Kolmogorov,Levy和Cramer-von Mises距离。距离的导出表达式用于为Dirichlet过程的浓度参数选择合适的值。这些工具也可用于拟合优度测试。包括说明性示例和仿真结果。

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