Evidence and Credibility: Full Bayesian Significance Test for Precise Hypotheses

Pereira, Carlos Alberto de Bragança; Stern, Julio Michael

doi:10.3390/e1040099

Cited by 117 publications

(57 citation statements)

References 16 publications

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“…It is consistent with the recommendation of [20]. The second method is based on an application of the Full Bayesian Significance Test (FBS Test) [21,22]. In order to verify the hypothesis about existing jumps, we could test the hypothesis H 0 : Z 1 = 0,. .…”

Section: Empirical Results -Jump Detectionsupporting

confidence: 52%

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Kostrzewski¹

2012

Acta Phys. Pol. B

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In this research two methods of detecting jumps are presented. One is based on the nonparametric approach, whereas the other -on the JD(M )J model. Bayesian inference is applied to detect jumps in the JD(M )J model. Intraday and daily rates of return are under consideration. The empirical results imply the existence of jumps. The information on existing jumps is exploited in a forecasting experiment focused on Value at Risk predictions.

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Section: Empirical Results -Jump Detectionsupporting

confidence: 52%

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Kostrzewski¹

2012

Acta Phys. Pol. B

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“…For example, agnostic tests based on frequentist confidence intervals control family wise error. Similarly, agnostic tests based on posterior density regions are shown to be an extension of the Full Bayesian Significance Test [11].…”

Section: Final Remarksmentioning

confidence: 93%

“…of the posterior distribution of θ, given x. For each hypothesis A P σpΘq, let T A x " # θ P Θ : f pθ|xq ą sup θPA f pθ|xq + be the set tangent to the null hypothesis and let ev x pAq " 1´Ppθ P T A x |xq be the Pereira-Stern evidence value for A [11]. Let c 1 , c 2 P p0, 1q, with c 1 ě c 2 , be fixed thresholds.…”

Section: Example 4 (Fbst Ats)mentioning

confidence: 99%

The Logical Consistency of Simultaneous Agnostic Hypothesis Tests

Esteves

Izbicki

Stern

et al. 2016

Entropy

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Simultaneous hypothesis tests can fail to provide results that meet logical requirements. For example, if A and B are two statements such that A implies B, there exist tests that, based on the same data, reject B but not A. Such outcomes are generally inconvenient to statisticians (who want to communicate the results to practitioners in a simple fashion) and non-statisticians (confused by conflicting pieces of information). Based on this inconvenience, one might want to use tests that satisfy logical requirements. However, Izbicki and Esteves shows that the only tests that are in accordance with three logical requirements (monotonicity, invertibility and consonance) are trivial tests based on point estimation, which generally lack statistical optimality. As a possible solution to this dilemma, this paper adapts the above logical requirements to agnostic tests, in which one can accept, reject or remain agnostic with respect to a given hypothesis. Each of the logical requirements is characterized in terms of a Bayesian decision theoretic perspective. Contrary to the results obtained for regular hypothesis tests, there exist agnostic tests that satisfy all logical requirements and also perform well statistically. In particular, agnostic tests that fulfill all logical requirements are characterized as region estimator-based tests. Examples of such tests are provided.

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“…Under the default setting a =1, Eq. (11) then simplifies to (de Bragança Pereira & Stern, 1999; Jeffreys, 1935; Wagenmakers, Lodewyckx, Kuriyal, & Grasman, 2010): where the left-hand side features binomial coefficients.The Bayes factor –or its inverse, which quantifies the evidence for , that is, – is a two-sided test. In experimental disciplines, however, researchers often have strong prior beliefs about the direction of the effect under scrutiny.…”

Section: Bayes Factors For Four Sampling Modelsmentioning

confidence: 99%

Default “Gunel and Dickey” Bayes factors for contingency tables

et al. 2016

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The analysis of R×C contingency tables usually features a test for independence between row and column counts. Throughout the social sciences, the adequacy of the independence hypothesis is generally evaluated by the outcome of a classical p-value null-hypothesis significance test. Unfortunately, however, the classical p-value comes with a number of well-documented drawbacks. Here we outline an alternative, Bayes factor method to quantify the evidence for and against the hypothesis of independence in R×C contingency tables. First we describe different sampling models for contingency tables and provide the corresponding default Bayes factors as originally developed by Gunel and Dickey (Biometrika, 61(3):545–557 (1974)). We then illustrate the properties and advantages of a Bayes factor analysis of contingency tables through simulations and practical examples. Computer code is available online and has been incorporated in the “BayesFactor” R package and the JASP program (jasp-stats.org).

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Evidence and Credibility: Full Bayesian Significance Test for Precise Hypotheses

Cited by 117 publications

References 16 publications

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Untitled

The Logical Consistency of Simultaneous Agnostic Hypothesis Tests

Default “Gunel and Dickey” Bayes factors for contingency tables

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