  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's 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 randomized controlled clinical trials investigating the association
between corticosteroids and mortality in hospitalized patients with COVID-19.
