A Bayesian χ2 test for goodness-of-fit
A Bayesian χ2 test for goodness-of-fit
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DOI：
10.1214/009053604000000616
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发表时间：
2004-12-01
影响因子：
4.5
通讯作者：
Johnson, VE
中科院分区：
文献类型：
--
作者：
Johnson, VE
本文介绍了经典的卡方检验的扩展，贝叶斯模型的评估。扩展，这基本上涉及到评估皮尔逊的拟合优度统计量的参数值从其后验分布，有一个重要的属性，它是渐近分布的卡方（2）随机变量的K - 1自由度，独立的基本参数向量的尺寸。通过检查该统计量的后验分布，获得全局拟合优度诊断。这些诊断的优点包括易于解释，计算方便和有利的功率特性。建议的诊断可以用来评估一个广泛的类贝叶斯模型的充分性，基本上只需要一个有限维的参数向量和条件独立的意见。
This article describes an extension of classical chi(2) goodness-of-fit tests to Bayesian model assessment. The extension, which essentially involves evaluating Pearson's goodness-of-fit statistic at a parameter value drawn from its posterior distribution, has the important property that it is asymptotically distributed as a chi(2) random variable on K - 1 degrees of freedom, independently of the dimension of the underlying parameter vector. By examining the posterior distribution of this statistic, global goodness-of-fit diagnostics are obtained. Advantages of these diagnostics include ease of interpretation, computational convenience and favorable power properties. The proposed diagnostics can be used to assess the adequacy of a broad class of Bayesian models, essentially requiring only a finite-dimensional parameter vector and conditionally independent observations.