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Full-Text Articles in Mathematics
Empirical Bayesian Approach To Testing Multiple Hypotheses With Separate Priors For Left And Right Alternatives, Naveen K. Bansal, Mehdi Maadooliat, Steven J. Schrodi
Empirical Bayesian Approach To Testing Multiple Hypotheses With Separate Priors For Left And Right Alternatives, Naveen K. Bansal, Mehdi Maadooliat, Steven J. Schrodi
Mathematics, Statistics and Computer Science Faculty Research and Publications
We consider a multiple hypotheses problem with directional alternatives in a decision theoretic framework. We obtain an empirical Bayes rule subject to a constraint on mixed directional false discovery rate (mdFDR≤α) under the semiparametric setting where the distribution of the test statistic is parametric, but the prior distribution is nonparametric. We proposed separate priors for the left tail and right tail alternatives as it may be required for many applications. The proposed Bayes rule is compared through simulation against rules proposed by Benjamini and Yekutieli and Efron. We illustrate the proposed methodology for two sets of …
Bayesian Decision Theoretic Approach To Directional Multiple Hypotheses Problems, Naveen K. Bansal, Klaus J. Miescke
Bayesian Decision Theoretic Approach To Directional Multiple Hypotheses Problems, Naveen K. Bansal, Klaus J. Miescke
Mathematics, Statistics and Computer Science Faculty Research and Publications
A multiple hypothesis problem with directional alternatives is considered in a decision theoretic framework. Skewness in the alternatives is considered, and it is shown that this skewness permits the Bayes rules to possess certain advantages when one direction of the alternatives is more important or more probable than the other direction. Bayes rules subject to constraints on certain directional false discovery rates are obtained, and their performances are compared with a traditional FDR rule through simulation. We also analyzed a gene expression data using our methodology, and compare the results to that of a FDR method.
Bayesian Analysis Of Hypothesis Testing Problems For General Population: A Kullback–Leibler Alternative, Naveen K. Bansal, Gholamhossein Hamedani, Ru Sheng
Bayesian Analysis Of Hypothesis Testing Problems For General Population: A Kullback–Leibler Alternative, Naveen K. Bansal, Gholamhossein Hamedani, Ru Sheng
Mathematics, Statistics and Computer Science Faculty Research and Publications
We consider a hypothesis problem with directional alternatives. We approach the problem from a Bayesian decision theoretic point of view and consider a situation when one side of the alternatives is more important or more probable than the other. We develop a general Bayesian framework by specifying a mixture prior structure and a loss function related to the Kullback–Leibler divergence. This Bayesian decision method is applied to Normal and Poisson populations. Simulations are performed to compare the performance of the proposed method with that of a method based on a classical z-test and a Bayesian method based on the …