NONINFORMATIVE BAYESIAN P-VALUES FOR TESTING MARGINAL HOMOGENEITY IN 2 × 2 CONTINGENCY TABLES
NONINFORMATIVE BAYESIAN P-VALUES FOR TESTING MARGINAL HOMOGENEITY IN 2 × 2 CONTINGENCY TABLES
复制标题
用于检验 2 × 2 列联表中边际同质性的非信息贝叶斯 P 值
DOI：
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发表时间：
2009
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通讯作者：
Ming
中科院分区：
文献类型：
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作者：
Lee;Ming
研究了多项式抽样格式下2 × 2列联表的边际齐性检验问题。从频率论的角度来看，McNemar的精确p值（p ME）是实践中最常用的p值，但对于小到中等样本量来说，它可能是保守的。另一方面，从贝叶斯的角度来看，可以通过使用适当的先验和后验分布来构造贝叶斯p值，分别称为先验预测p值（prior）和后验预测p值（ppost）。另一种贝叶斯p值称为部分后验预测p值（pppost），由[2]首先提出，它可以避免发生在ppost中的数据的双重使用。对于前一个问题，我们基于非信息一致先验推导出先验、ppost和pppost。在频率论意义上的一致性准则下，对先验、先验、先验、先验和先验进行了比较。数值结果表明，pppost在小样本量到中等样本量的情况下具有最佳的性能。
This article considers the problem of testing marginal homogeneity in 2 × 2 contingency tables under the multinomial sampling scheme. From the frequentist perspective, McNemar’s exact p-value (p ME ) is the most commonly used p-value in practice, but it can be conservative for small to moderate sample sizes. On the other hand, from the Bayesian perspective, one can construct Bayesian p-values by using the proper prior and posterior distributions, which are called the prior predictive p-value (pprior) and the posterior predictive p-value (ppost), respectively. Another Bayesian p-value is called the partial posterior predictive p-value (pppost), first proposed by [2], which can avoid the double use of the data that occurs in ppost. For the preceding problem, we derive pprior, ppost, and pppost based on the noninformative uniform prior. Under the criterion of uniformity in the frequentist sense, comparisons among pprior, pME , ppost and pppost are given. Numerical results show that pppost has the best performance for small to moderately large sample sizes.