Priors
Why use priors? People who are used to frequentist statistics sometimes feel bothered by priors. It helps to realize that all new knowledge is anyways influenced by other knowledge that we have. The Duhem-Quine thesis ("confirmation holism") says that no individual statement can be confirmed or disconfirmed by a test, only a set of statements can.
Put differently, if you were to use a frequentist paper as evidence for anything, you're implicitly using that background knowledge anyway, assumptions the researcher baked in without telling you, so if they specify prior beliefs, then that simply makes the research more honest and useful to you.
The paper may also contain a Sensitivity analysis: showing the influence of different priors on the conclusion.
A researcher may gather reasonable priors by way of Expert elicitation and/or Systematic review.