Beyond p < .05: a critical review of new Bayesian proposals for assessing the p-value.

This paper reviews recent contributions from a Bayesian-oriented perspective, after the ASA statement on p-values (2016). We classify proposals that (i) supplement the p-value; (ii) modify the p-value itself. In the first group, we review the Bayes factor, the False Positive risk, the rejection odds and the analysis of credibility from both Matthews' and Held's point of view. We also put forth and discuss a new index of credibility, about which we conduct a delimited simulation study. In the second group, we discuss Gannon's modification of the p-value based on the Bayes factor and the second-generation p-value. The theory is illustrated with two case studies on pharmacotherapy in infectious diseases. Contemporary authors still refer to the p-value as a statistical indicator but have abandoned the perspective of evaluating p-values with fixed thresholds. Statistical societies worldwide should target new strategies to disseminate the debate on p-values in all applied fields of knowledge, as well as they may promote the use of different statistical procedures to supplement p-values.

Reverse-Bayes methods for evidence assessment and research synthesis

It is now widely accepted that the standard inferential toolkit used by the scientific research community-null-hypothesis significance testing (NHST)-is not fit for purpose. Yet despite the threat posed to the scientific enterprise, there is no agreement concerning alternative approaches for evidence assessment. This lack of consensus reflects long-standing issues concerning Bayesian methods, the principal alternative to NHST. We report on recent work that builds on an approach to inference put forward over 70 years ago to address the well-known "Problem of Priors" in Bayesian analysis, by reversing the conventional prior-likelihood-posterior ("forward") use of Bayes' theorem. Such Reverse-Bayes analysis allows priors to be deduced from the likelihood by requiring that the posterior achieve a specified level of credibility. We summarise the technical underpinning of this approach, and show how it opens up new approaches to common inferential challenges, such as assessing the credibility of scientific findings, setting them in appropriate context, estimating the probability of successful replications, and extracting more insight from NHST while reducing the risk of misinterpretation. We argue that Reverse-Bayes methods have a key role to play in making Bayesian methods more accessible and attractive for evidence assessment and research synthesis. As a running example we consider a recently published meta-analysis from several randomised controlled trials (RCTs) investigating the association between corticosteroids and mortality in hospitalised patients with COVID-19. (PsycInfo Database Record (c) 2022 APA, all rights reserved)

Reverse-Bayes methods for evidence assessment and research synthesis.

It is now widely accepted that the standard inferential toolkit used by the scientific research community-null-hypothesis significance testing (NHST)-is not fit for purpose. Yet despite the threat posed to the scientific enterprise, there is no agreement concerning alternative approaches for evidence assessment. This lack of consensus reflects long-standing issues concerning Bayesian methods, the principal alternative to NHST. We report on recent work that builds on an approach to inference put forward over 70 years ago to address the well-known "Problem of Priors" in Bayesian analysis, by reversing the conventional prior-likelihood-posterior ("forward") use of Bayes' theorem. Such Reverse-Bayes analysis allows priors to be deduced from the likelihood by requiring that the posterior achieve a specified level of credibility. We summarise the technical underpinning of this approach, and show how it opens up new approaches to common inferential challenges, such as assessing the credibility of scientific findings, setting them in appropriate context, estimating the probability of successful replications, and extracting more insight from NHST while reducing the risk of misinterpretation. We argue that Reverse-Bayes methods have a key role to play in making Bayesian methods more accessible and attractive for evidence assessment and research synthesis. As a running example we consider a recently published meta-analysis from several randomised controlled trials (RCTs) investigating the association between corticosteroids and mortality in hospitalised patients with COVID-19.