Bayes' theorem — posterior proportional to prior times
likelihood — frames belief as a probability that
updates with evidence. A Bayesian argument refuses the
false binary of accept-or-reject: every hypothesis has
a probability, every observation shifts that
probability, and the right summary is a posterior
distribution rather than a p-value. The tradition
(Laplace, Jeffreys, Cox, Jaynes) elevates this into a
complete theory of rational inference. Methodologically
it privileges explicit priors, likelihood functions,
and decision-theoretic summaries (credible intervals,
Bayes factors, posterior predictive checks). A
Bayesian claimant in a debate will press: what is your
prior, what is your likelihood, and what is the
posterior — not "is it significant" but "how sure are
we now?" The characteristic move is to convert a
yes/no scientific question into a graded posterior with
a quantified uncertainty. Weakness: priors can be
smuggled in to dominate sparse data, and computational
demands can be heavy.