A new Bayesian procedure for testing point null hypotheses

Yin, Yuliang

doi:10.1007/s00180-011-0252-6

Cited by 6 publications

(17 citation statements)

References 16 publications

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“…For the purpose of this discussion, we shall refer to the methodology of Yin [1] as the New Bayesian measure of evidence. The Metropolis-Hastings algorithm was used for the simulation with a thinning length of 12.…”

Section: Simulation Results and Discussionmentioning

confidence: 99%

“…In this paper, we looked at the Bayesian analysis of the Behrens-Fisher problem using the methodology of Yin [1]…”

Section: Discussionmentioning

confidence: 99%

“…Ghosh and Kim [17] proposed an approach of constructing a prior different from Jeffreys' independent prior that leads to a credible interval whose asymptotic coverage probability matches the frequentist coverage probability more accurately than Jeffreys' interval. Yin [1]…”

Section: Literature Reviewmentioning

confidence: 99%

“…For discussions and arguments concerning Lindley's paradox, see Spanos [4] and Robert [5]. As an extension of the methodology of Yin [1], Yin and Li [2] made an attempt to solve the Behrens-Fisher Problem as well as Lindley's Paradox using a noninformative prior. In this work, we propose to examine the performance of the methodology of Yin [1] in solving simultaneously, the Behrens-Fisher problem and Lindley's paradox when Gamma priors are assigned to the unknown variances.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Analysis of the Behrens-Fisher Problem under a Gamma Prior

Goltong¹,

Doguwa²

2018

OJS

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Yin [1] has developed a new Bayesian measure of evidence for testing a point null hypothesis which agrees with the frequentist p-value thereby, solving Lindley's paradox. Yin and Li [2] extended the methodology of Yin [1] to the case of the Behrens-Fisher problem by assigning Jeffreys' independent prior to the nuisance parameters. In this paper, we were able to show both analytically and through the results from simulation studies that the methodology of Yin [1] solves simultaneously, the Behrens-Fisher problem and Lindley's paradox when a Gamma prior is assigned to the nuisance parameters.

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Section: Simulation Results and Discussionmentioning

confidence: 99%

“…In this paper, we looked at the Bayesian analysis of the Behrens-Fisher problem using the methodology of Yin [1]…”

Section: Discussionmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bayesian Analysis of the Behrens-Fisher Problem under a Gamma Prior

Goltong¹,

Doguwa²

2018

OJS

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“…More discussions and arguments concerning Lindley's paradox, can be found in [3], [4] and [2]. [5] developed a Bayesian hypothesis testing framework that solves Lindley's paradox in a one sample case. Using Jeffreys' independent prior, [6] extended the methodology of [5] to solve the Behrens-Fisher Problem so as to avoid Lindleys' Paradox.…”

Section: Introductionmentioning

confidence: 99%

On Analysis of the Behrens-Fisher Problem Based on Bayesian Evidence

Zaria¹,

Nigéria²

2019

OJS

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New multiple testing method under no dependency assumption, with application to multiple comparisons problem

Wang

Yong³

2014

Stat Papers

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Traditional multiple hypotheses testing mainly focuses on constructing stepwise procedures under some error rate control, such as familywise error rate (FWER), false discovery rate, and so forth. However, most of these procedures are obtained in independent case, and when there exists correlation across tests, the dependency may increase or decrease the chance of false rejections. In this paper, a totally different testing method is proposed, which doesn't focus on specific error control, but pays attention to the overall performance of the collection of hypotheses and the structure utilization among hypotheses. Since the main purpose of multiple testing is to pick out the false ones from the whole hypotheses and present a rejection set, motivated by the principle of simple hypothesis testing, we give the final testing result based on the estimation of the set of all the true null hypotheses. Our method can be applied in any dependent case provided that a reasonable p-value can be obtained for each intersection hypothesis. We illustrate the new procedures with application to multiple comparisons problems. Theoretical results show the consistency of our method, and investigate their FWER behavior. Simulation results suggest that our procedures have a better overall performance than some existing procedures in dependent cases, especially in the total number of type I and type II errors.

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A new Bayesian procedure for testing point null hypotheses

Cited by 6 publications

References 16 publications

Bayesian Analysis of the Behrens-Fisher Problem under a Gamma Prior

Bayesian Analysis of the Behrens-Fisher Problem under a Gamma Prior

On Analysis of the Behrens-Fisher Problem Based on Bayesian Evidence

New multiple testing method under no dependency assumption, with application to multiple comparisons problem

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