Posterior probability is the updated probability of a hypothesis after incorporating observed evidence. It is computed via Bayes theorem: P(H|E) = P(E|H) · P(H) / P(E), where P(H) is the prior probability of the hypothesis, P(E|H) is the likelihood of the evidence given the hypothesis, and P(E) is the marginal probability of the evidence. The parameters are: the hypothesis space, the prior distribution, the likelihood function, and the observed evidence. It persists through the mathematical formalism of Bayesian inference and its applications in statistics, machine learning, and decision theory under uncertainty. [formal: probabilis posterior | substrate: mind | horizon: a moment | explicit: yes | epoch: 0.01]
Accepted ontology entry
posterior probability
Posterior probability is the updated probability of a hypothesis after incorporating observed evidence. It is computed via Bayes theorem: P(H|E) = P(E|H) · P(H) / P(E), where P(H) is the prior probability of the hypothesis, P(E|H) is the l…
Definition
Why it is in scope
A human-made probabilistic concept representing the updated degree of belief in a hypothesis after observing evidence. It is the output of Bayes' theorem — the conditional probability of a hypothesis given observed data — and persists through mathematical formalism, Bayesian statistical practice, and machine learning inference protocols.
Names and aliases
- posterior probabilityen · CANONICAL
Relations from this entry
- cmsfrrt7e00ayqszgbbhie7ekDEPENDS_ON →
Posterior probability is computed via Bayes theorem: P(H|E) = P(E|H)P(H)/P(E). Remove Bayes theorem and posterior probability has no mechanism for computation. The removal test is positive.
- cmsf6w1ek06ms3vv3snhiwxwlDEPENDS_ON →
Posterior probability P(H|E) = P(E|H)P(H)/P(E) is computed entirely within probability theory. Remove probability theory — the measure-theoretic foundation of probability spaces, conditional probabilities, and Bayes' rule — and posterior probability has no mathematical machinery to operate. The removal test passes: X stops operating without Y.
- marginal-likelihoodDEPENDS_ON →
Posterior probability p(theta|x) = p(x|theta)pi(theta)/p(x) requires the marginal likelihood p(x) as its normalizing denominator. Without marginal likelihood, posterior probabilities cannot be computed at all. The removal of marginal likelihood means the posterior stops operating.
Relations to this entry
No accepted relations in this direction.
Record identity
- Created
- Aug 5, 2026, 8:40 AM UTC
- Content hash
- 8563009c5e1c9a56693c54d31976e0377be440b556a6e7613a6035a65e13fd3e