Bayesian hypothesis testing for the distribution of insurance claim counts using the Gibbs sampler

A new Bayesian approach for multiple satellite faults detection and exclusion is proposed by introducing a classification variable to each satellite observation. If we treat this classification variable as random and assume a prior distribution for it, then a rule for satellite fault detection and exclusion based on the posterior probabilities of the classification variables is constructed under the framework of Bayesian hypothesis testing. Secondly, the Gibbs sampler is introduced to compute the posterior probabilities of the classification variables. Then the implementation for a Bayesian Receiver Autonomous Integrity Monitoring (RAIM) algorithm is designed with the Gibbs sampler. Finally, different schemes are designed to evaluate the performance of the new Bayesian RAIM algorithm in the case of multiple faults. We compare the method in this paper with the Range Consensus (RANCO) method. Experiments illustrate that the proposed algorithm in this paper is capable of detecting and eliminating multiple satellite faults, and the probability of correctly detecting faults is high.

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Statistical evidence and sample size determination for Bayesian hypothesis testing

Journal of Statistical Planning and Inference ◽

10.1016/s0378-3758(03)00198-8 ◽

2004 ◽

Vol 124 (1) ◽

pp. 121-144 ◽

Cited By ~ 24

Author(s):

Fulvio De Santis

Keyword(s):

Hypothesis Testing ◽

Sample Size ◽

Statistical Evidence ◽

Sample Size Determination ◽

Size Determination ◽

Bayesian Hypothesis Testing

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A Critical Evaluation of the FBST ev for Bayesian Hypothesis Testing

Computational Brain & Behavior ◽

10.1007/s42113-021-00109-y ◽

2021 ◽

Author(s):

Alexander Ly ◽

Eric-Jan Wagenmakers

Keyword(s):

Hypothesis Testing ◽

Null Hypothesis ◽

Alternative Hypothesis ◽

Critical Evaluation ◽

Significance Test ◽

Bayesian Hypothesis Testing ◽

Absence Of Evidence ◽

Evidence Of Absence ◽

Foregone Conclusion

AbstractThe “Full Bayesian Significance Test e-value”, henceforth FBST ev, has received increasing attention across a range of disciplines including psychology. We show that the FBST ev leads to four problems: (1) the FBST ev cannot quantify evidence in favor of a null hypothesis and therefore also cannot discriminate “evidence of absence” from “absence of evidence”; (2) the FBST ev is susceptible to sampling to a foregone conclusion; (3) the FBST ev violates the principle of predictive irrelevance, such that it is affected by data that are equally likely to occur under the null hypothesis and the alternative hypothesis; (4) the FBST ev suffers from the Jeffreys-Lindley paradox in that it does not include a correction for selection. These problems also plague the frequentist p-value. We conclude that although the FBST ev may be an improvement over the p-value, it does not provide a reasonable measure of evidence against the null hypothesis.

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