论文标题
通过将p值解释为后概率，使林德利的悖论神秘化
Demystify Lindley's Paradox by Interpreting P-value as Posterior Probability
论文作者
论文摘要
在假设测试框架中，通常计算P值以确定无效假设的排斥。另一方面，贝叶斯的方法通常计算出无效假设的后验概率以评估其合理性。我们重新审视了林德利的悖论（Lindley，1957年），并通过将两面假设作为沿着相反方向的两个单方面假设的组合组合来结合贝叶斯和频繁的假设测试程序之间的矛盾结果。这自然可以规避将点质量分配给NULL和使用局部或非本地先验分布的选择的歧义。由于p值仅取决于观察到的数据而没有包含任何先前的信息，因此我们考虑非信息性先验分布，以进行与p值进行公平的比较。可以建立p值和贝叶斯后概率的等效性，以调和林德利的悖论。大量的模拟研究是使用多元正常数据和随机效应模型进行的，以检查p值和后验概率之间的关系。
In the hypothesis testing framework, p-value is often computed to determine rejection of the null hypothesis or not. On the other hand, Bayesian approaches typically compute the posterior probability of the null hypothesis to evaluate its plausibility. We revisit Lindley's paradox (Lindley, 1957) and demystify the conflicting results between Bayesian and frequentist hypothesis testing procedures by casting a two-sided hypothesis as a combination of two one-sided hypotheses along the opposite directions. This can naturally circumvent the ambiguities of assigning a point mass to the null and choices of using local or non-local prior distributions. As p-value solely depends on the observed data without incorporating any prior information, we consider non-informative prior distributions for fair comparisons with p-value. The equivalence of p-value and the Bayesian posterior probability of the null hypothesis can be established to reconcile Lindley's paradox. Extensive simulation studies are conducted with multivariate normal data and random effects models to examine the relationship between the p-value and posterior probability.
