12月17日 | Dr Guosheng Yin:Demystify Lindley’s Paradox: Reconcile P-value and the Posterior Probability

时间:2019-12-15浏览:245设置

时间:2019年12月17日(周二)15:00-16:00

地点:中北校区理科大楼1716报告厅

题目:Demystify Lindley’s Paradox: Reconcile P-value and the Posterior Probability

主讲人:Dr Guosheng Yin(Patrick S C Poon Professor   Department of Statistics and Actuarial Science,The University of Hong Kong)

摘要:

In the hypothesis testing framework, p-value is often computed and compared with the nominal significance level of 0.05 to determine whether or not to reject the null hypothesis. 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 based on a new notion of two-sided posterior probability. We propose to cast a two-sided hypothesis as a combination of two one-sided hypotheses along the opposite directions, which can naturally circumvent the difficulties of using local or non-local prior distributions. Under non-informative prior distributions (this is to be fair to p-value, as p-value solely depends on the observed data without incorporating any prior information), we establish the equivalence of p-value and the Bayesian posterior probability of the null hypothesis. We reclaim p-value an explicit interpretation of how strong the data support the null. Extensive simulation studies are conducted to demonstrate the Bayesian posterior probability interpretation for the p-value. Multivariate normal data and random effects models are also considered to examine the relationship between the p-value and posterior probability under various hypothesis tests.

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