Bayesian probability

Bayesian probability represents uncertainty about propositions or parameters as probabilities, updated when evidence arrives using Bayes' theorem.

Bayes' theorem: A rule relating conditional probabilities that updates a hypothesis's probability using new evidence. It formalizes how Bayesian probability revises beliefs when evidence is observed.
Probability: A numerical measure of the likelihood of an event, ranging from zero to one. Bayesian probability is one interpretation of this broader mathematical quantity.
Thomas Bayes: An English clergyman and mathematician whose posthumous essay presented an early form of Bayes' theorem. His work gave the interpretation its name and an early mathematical foundation.
Bayesian inference: A method of statistical inference that combines prior distributions with data through Bayes' theorem. It is the principal framework for applying Bayesian probability to observed data.
Objective Bayesianism: A view that seeks principled or uniquely justified Bayesian priors rather than treating them as freely personal. It challenges interpretations that leave prior probabilities largely dependent on an individual's information.
Prior probability: A probability distribution expressing uncertainty before incorporating specified evidence. It encodes the uncertainty that Bayesian updating begins with.
Conditionalization: The operation of revising probabilities by conditioning on newly learned evidence. It is the standard rule for changing Bayesian beliefs after observations.
Richard Price: A Welsh philosopher and mathematician who edited and published Bayes's essay after his death. His editorial work brought Bayes's result into public scientific discussion.
Bayesian statistics: Statistical methods that represent unknown quantities probabilistically and update distributions with data. It uses Bayesian probability as the basis for estimation and uncertainty statements.
Subjective Bayesianism: A view that treats probabilities as rational degrees of belief constrained by coherence and evidence. It emphasizes personal belief, a central but contested reading of Bayesian probability.

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