Prior probability is a statistical concept representing the initial degree of belief in a hypothesis before observing new evidence. Its parameters are (1) a hypothesis or set of hypotheses, (2) a probability value or distribution expressing initial confidence, and (3) the context of a Bayesian inference procedure. It persists through Bayesian statistical practice, notation conventions (P(H) for hypothesis H), and the pedagogical framework of Bayesian reasoning. [formal: prior probability | substrate: mind | horizon: a life | explicit: yes | epoch: 0.14]
Accepted ontology entry
prior probability
Prior probability is a statistical concept representing the initial degree of belief in a hypothesis before observing new evidence. Its parameters are (1) a hypothesis or set of hypotheses, (2) a probability value or distribution expressin…
Definition
Why it is in scope
A human-made statistical concept representing the initial degree of belief in a hypothesis before observing new evidence. In Bayesian statistics, it is denoted P(H) for hypothesis H and serves as the starting point for Bayes' theorem: posterior = likelihood × prior / evidence. Priors encode existing knowledge or assumptions and are updated to posterior probabilities upon observing data. Priors can be informative (based on substantive knowledge), non-informative (designed to exert minimal influence), or reference (objective Bayesian choice). The formalization of prior probability is attributed to Thomas Bayes and Pierre-Simon Laplace.
Names and aliases
- prior probabilityen · CANONICAL
Relations from this entry
- cmsfrrt7e00ayqszgbbhie7ekDERIVED_FROM →
Prior probability as a formal statistical concept emerged within Bayesian inference. Bayes theorem (P(H|E) = P(E|H)P(H)/P(E)) introduced the notion of a prior P(H) — a probability distribution representing beliefs before observing evidence. Bayes theorem existed first and provided the framework from which 'prior probability' derives.
- cmsf6w1ek06ms3vv3snhiwxwlDERIVED_FROM →
Prior probability is a specific concept within probability theory. Probability theory (Pascal/Fermat, 1654) existed first and fed into the development of prior probability as a Bayesian concept (Bayes' theorem, 1763). Which existed first? Probability theory predates prior probability by over a century.
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- Aug 5, 2026, 7:56 AM UTC
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