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Bayesian approaches to simultaneous ...

Chen, Jie.

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Bayesian approaches to simultaneous testing of multiple hypotheses.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Bayesian approaches to simultaneous testing of multiple hypotheses./
Author:	Chen, Jie.
Description:	136 p.
Notes:	Source: Dissertation Abstracts International, Volume: 65-03, Section: B, page: 1387.
Contained By:	Dissertation Abstracts International65-03B.
Subject:	Statistics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3125523

Bayesian approaches to simultaneous testing of multiple hypotheses.
Chen, Jie.

Bayesian approaches to simultaneous testing of multiple hypotheses. - 136 p.

Source: Dissertation Abstracts International, Volume: 65-03, Section: B, page: 1387.

Thesis (Ph.D.)--Temple University, 2004.

Two different Bayesian approaches are proposed for simultaneous testing of multiple hypotheses. They are a stepwise procedure using stepwise Bayes factors and a single-step average error rate procedure measuring the risks of false rejections and false non-rejections.Subjects--Topical Terms:

517247
Statistics.

Bayesian approaches to simultaneous testing of multiple hypotheses.
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245 1 0 $a Bayesian approaches to simultaneous testing of multiple hypotheses.
300 $a 136 p.
500 $a Source: Dissertation Abstracts International, Volume: 65-03, Section: B, page: 1387.
500 $a Chair: Sanat K. Sarkar.
502 $a Thesis (Ph.D.)--Temple University, 2004.
520 $a Two different Bayesian approaches are proposed for simultaneous testing of multiple hypotheses. They are a stepwise procedure using stepwise Bayes factors and a single-step average error rate procedure measuring the risks of false rejections and false non-rejections.
520 $a Bayesian testing of multiple hypotheses often requires consideration of all configurations of the true and false null hypotheses, which is a difficult task when the number of hypotheses is even moderately large. In this research, a Bayesian stepwise approach is proposed. After ordering the null hypotheses in terms of their marginal Bayes factors, a determination is made of all possible configurations of true and false ordered null hypotheses. The most plausible configuration is then tested in a stepwise manner starting with the intersection of all the null hypotheses. The present Bayesian approach provides considerable reduction in the size of the set of families within which we restrict our posterior search for the "right" family of true and false null hypotheses, from 2k to only k + 1, given k null hypotheses. The hierarchical prior structure is considered in general. The stepwise Bayes factors are derived in situations involving point null hypotheses and those arising in one-sided testing problems under normal distributional settings. Our procedure when applied to three different examples results in conclusions that are similar to those obtained using an analogous frequentist approach.
520 $a The original definition of the FDR can be understood as the frequentist risk of false rejections conditional on the unknown parameter theta and the Bayesian posterior FDR is conditioned on the observed data T. From Bayesian decision theoretic point of view, it seems natural to take into account the uncertainty in both parameter and data. In this spirit, we propose the Average FDR (AFDR) and Average FNR (AFNR) approaches in which the frequentist risks of false rejections and false non-rejections are averaged out with respect to some prior distribution of parameter theta. A linear combination of the AFDR and AFNR, called the Average Bayes Error Rate (ABER), is considered as the overall risk of misclassification. Finally, the AFDR and AFNR are illustrated in an example where objective and subjective Bayesian hypotheses are formulated.
590 $a School code: 0225.
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790 1 0 $a Sarkar, Sanat K., $e advisor
790 $a 0225
791 $a Ph.D.
792 $a 2004
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