專題演講 主講人：胡膺期教授 (George Mason University, U.S.A.)
題 目：Empirical Bayes Analysis and Selection Bias
主講人：胡膺期教授 (Professor Inchi Hu)
George Mason University, U.S.A.
時 間：112年1月6日(星期五)上午10:40-11:30
(上午10:20-10:40茶會於交大統計所428室舉行)
地 點：綜合一館427室
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摘要
In a thought-provoking paper, Efron (2011) investigated the merit and limitation of an empirical Bayes method to correct selection bias based on Tweedie's formula first reported in Robbins (1956). The exceptional virtue of Tweedie's formula lies in its representation of selection bias as a simple function of the derivative of log marginal likelihood. Since the marginal likelihood and its derivative can be estimated from the data directly without invoking prior information, bias correction can be carried out conveniently. We propose a Bayesian hierarchical model for chi-squared data such that the resulting Tweedie's formula has the same virtue. Because the family of noncentral chi-squared distributions, the common alternative distributions for chi-squared tests, does not constitute an exponential family, our results cannot be obtained by extending existing results. Furthermore, the corresponding Tweedie's formula manifests new phenomena quite different from those of the normal distribution and suggests new ways of analysing chi-squared data.
