← Pantheon · bayes

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.