Can a significance test be genuinely Bayesian?

Pereira, Carlos Alberto de Bragança; Stern, Julio Michael; Wechsler, Sergio

doi:10.1214/08-ba303

Cited by 106 publications

(152 citation statements)

References 25 publications

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“…For the negative binomial, the two observed points will produce different significance levels and probabilities of both kinds of errors. For the first (second) sample, one stops observing whenever the number of successes reaches 3 Equation (11). For the first result, we have α = 0.18, β = 0.4 and P = 0.0; for the second, α = 0.12, β = 0.33, and P = 0.01.…”

Section: Example 3-test For One Proportion and The Likelihood Principlementioning

confidence: 99%

“…In a genuinely Bayesian context, the authors of [9] introduced the index e (e-value, e for evidence) as an alternative to the classical p-value, which we write with a lower-case "p". A correction to make the null hypothesis invariant under transformations was presented in [10], and a more theoretical review can be seen in [11,12]. The e-value was the basis of the solution of an astrophysical problem described in [13].…”

Section: Introductionmentioning

confidence: 99%

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Hypothesis Tests for Bernoulli Experiments: Ordering the Sample Space by Bayes Factors and Using Adaptive Significance Levels for Decisions

Pereira

Nakano

Fossaluza

et al. 2017

Entropy

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Abstract:The main objective of this paper is to find the relation between the adaptive significance level presented here and the sample size. We statisticians know of the inconsistency, or paradox, in the current classical tests of significance that are based on p-value statistics that are compared to the canonical significance levels (10%, 5%, and 1%): "Raise the sample to reject the null hypothesis" is the recommendation of some ill-advised scientists! This paper will show that it is possible to eliminate this problem of significance tests. We present here the beginning of a larger research project. The intention is to extend its use to more complex applications such as survival analysis, reliability tests, and other areas. The main tools used here are the Bayes factor and the extended Neyman-Pearson Lemma.

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Section: Example 3-test For One Proportion and The Likelihood Principlementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hypothesis Tests for Bernoulli Experiments: Ordering the Sample Space by Bayes Factors and Using Adaptive Significance Levels for Decisions

Pereira

Nakano

Fossaluza

et al. 2017

Entropy

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show abstract

“…Therefore, if the tangential set has high posterior probability, the evidence in favor of Ω 0 is small; if it has low posterior probability, the evidence against Ω 0 is small, see [13].…”

Section: Hypotheses Testingmentioning

confidence: 99%

A Simulation-Based Study on Bayesian Estimators for the Skew Brownian Motion

Barahona

Rifo

Sepúlveda

et al. 2016

Entropy

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Abstract:In analyzing a temporal data set from a continuous variable, diffusion processes can be suitable under certain conditions, depending on the distribution of increments. We are interested in processes where a semi-permeable barrier splits the state space, producing a skewed diffusion that can have different rates on each side. In this work, the asymptotic behavior of some Bayesian inferences for this class of processes is discussed and validated through simulations. As an application, we model the location of South American sea lions (Otaria flavescens) on the coast of Calbuco, southern Chile, which can be used to understand how the foraging behavior of apex predators varies temporally and spatially.

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“…In order to avoid the Jeffreys-Lindley paradox, the measure of evidence (EV ) of the full Bayesian significance test (FBST) of Stern (1999, 2001) can be considered; see also Madruga et al (2001Madruga et al ( , 2003 and Pereira et al (2008). Following Cabras et al (2013), consider the set…”

Section: Tail Area Approximations For a Measure Of Evidencementioning

confidence: 99%

A note on approximate Bayesian credible sets based on modified loglikelihood ratios

Ventura

Ruli

Racugno

2013

Statistics & Probability Letters

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Abstract:Asymptotic arguments are widely used in Bayesian inference, and in recent years there has been considerable developments of the so-called higherorder asymptotics. This theory provides very accurate approximations to posterior distributions, and to related quantities, in a variety of parametric statistical problems, even for small sample sizes. The aim of this contribution is to discuss recent advances in approximate Bayesian computations based on the asymptotic theory of modified loglikelihood ratios, both from theoretical and practical point of views. Results on third-order approximations for univariate posterior distributions, also in the presence of nuisance parameters, are reviewed and a new formula for a vector parameter of interest is presented. All these approximations may routinely be applied in practice for Bayesian inference, since they require little more than standard likelihood quantities for their implementation, and hence they may be available at little additional computational cost over simple first-order approximations. Moreover, these approximations give rise to a simple simulation scheme, alternative to MCMC, for Bayesian computation of marginal posterior distributions for a scalar parameter of interest. In addition, they can be used for testing precise null hypothesis and to define accurate Bayesian credible sets. Some illustrative examples are discussed, with particular attention to the use of matching priors.

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Can a significance test be genuinely Bayesian?

Cited by 106 publications

References 25 publications

Hypothesis Tests for Bernoulli Experiments: Ordering the Sample Space by Bayes Factors and Using Adaptive Significance Levels for Decisions

Hypothesis Tests for Bernoulli Experiments: Ordering the Sample Space by Bayes Factors and Using Adaptive Significance Levels for Decisions

A Simulation-Based Study on Bayesian Estimators for the Skew Brownian Motion

A note on approximate Bayesian credible sets based on modified loglikelihood ratios

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