  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. 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 to the scientific community. 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.
