Journal
SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES
Volume 16, Issue 1, Pages 566-584Publisher
SPRINGER INT PUBL AG
DOI: 10.1007/s40863-020-00171-7
Keywords
Bayesian inference; Hypothesis testing; Foundations of statistics
Categories
Funding
- CNPq - the Brazilian National Counsel of Technological and Scientific Development [PQ 302767/2017-7, PQ 301892/2015-6]
- FAPESP - the State of Sao Paulo Research Foundation [CEPID Shell-RCGI 2014/50279-4, CEPID CeMEAI 2013/07375-0]
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This article gives a survey of the e-value and its application, which is a statistical significance measure in Bayesian inference. The e-value and the accompanying FBST comply with best principles of Bayesian inference and exhibit powerful logical and algebraic properties. They are also convenient for dealing with sharp or precise hypotheses. The FBST outperforms traditional tests of hypotheses in many practical applications of statistical modeling and operations research.
This article gives a survey of the e-value, a statistical significance measure a.k.a. the evidence rendered by observational data, X, in support of a statistical hypothesis, H, or, the other way around, the epistemic value of H given X. The e-value and the accompanying FBST, the Full Bayesian Significance Test, constitute the core of a research program that was started at IME-USP, is being developed by over 20 researchers worldwide, and has, so far, been referenced by over 200 publications. The e-value and the FBST comply with the best principles of Bayesian inference, including the likelihood principle, complete invariance, asymptotic consistency, etc. Furthermore, they exhibit powerful logic or algebraic properties in situations where one needs to compare or compose distinct hypotheses that can be formulated either in the same or in different statistical models. Moreover, they effortlessly accommodate the case of sharp or precise hypotheses, a situation where alternative methods often require ad hoc and convoluted procedures. Finally, the FBST has outstanding robustness and reliability characteristics, outperforming traditional tests of hypotheses in many practical applications of statistical modeling and operations research.
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