Bayesian epistemology

Bayesian epistemology represents degrees of belief with probabilities and models how evidence should change them. It connects rational belief to probability theory and conditionalization.

Bayes' theorem: A rule relating conditional probabilities that updates a hypothesis's probability using evidence. It supplies the mathematical rule for revising belief after observing evidence.
Probability theory: The mathematical study of probability assignments and the relations they must satisfy. Bayesian epistemology uses its axioms to constrain rational degrees of belief.
Frequentist inference: A statistical approach that evaluates procedures through their long-run behavior under repeated sampling. It contrasts with Bayesian inference by avoiding probabilities for hypotheses in its standard account.
Bayesian inference: A statistical method that combines prior distributions with likelihoods to obtain posterior distributions. It applies Bayesian principles to estimate unknown quantities from data.
Problem of priors: The challenge of selecting initial probabilities when no uniquely justified prior is available. Different priors can yield different conclusions even after the same evidence.
Bayesian conditionalization: A rule that updates a probability distribution by conditioning on newly learned evidence. It formalizes the central belief update when evidence is treated as certain.
Conditional probability: The probability of an event given that another event is known to have occurred. Belief revision depends on how likely evidence is under the hypotheses considered.
Falsificationism: A philosophy of science that emphasizes testing theories through attempts to refute them. It stresses severe tests rather than representing evidential support as graded probability.
Bayesian confirmation theory: An account of evidential support that measures confirmation through changes in probability. It uses Bayesian updating to analyze when evidence supports a hypothesis.
Old evidence problem: The challenge of explaining how already-known evidence can confirm a newly proposed theory. Simple conditionalization appears unable to increase belief from evidence learned earlier.

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