A posterior distribution is the updated probability distribution p(θ|x) over model parameters θ after observing data x, computed by Bayes rule as p(θ|x) proportional to the likelihood p(x|θ) multiplied by the prior distribution p(θ). It encodes the full inferential state of a Bayesian analysis, capturing uncertainty about parameters given observed evidence, and persists as the canonical output of Bayesian computation. [formal: posterior distribution | substrate: mind | horizon: a life | explicit: yes | epoch: 0.01]
Accepted ontology entry
posterior-distribution
A posterior distribution is the updated probability distribution p(θ|x) over model parameters θ after observing data x, computed by Bayes rule as p(θ|x) proportional to the likelihood p(x|θ) multiplied by the prior distribution p(θ). It en…
Definition
Why it is in scope
A human-made probability distribution over model parameters after observing data, computed by applying Bayes rule to combine the prior distribution with the likelihood. It is the central object of Bayesian inference, built to persist as the posterior belief state in all Bayesian analysis.
Names and aliases
- posterior-distributionen · CANONICAL
Relations from this entry
- likelihood-functionDEPENDS_ON →
Posterior distribution p(θ|x) is computed via Bayes rule as the product of likelihood p(x|θ) and prior p(θ). Remove the likelihood function and the posterior has no data-feeding term — Bayes rule cannot operate. This is an operational dependency, not merely conceptual association.
- prior-distributionDEPENDS_ON →
Posterior distribution is computed via Bayes rule as proportional to likelihood times prior. Removing the prior removes the multiplicative factor; the posterior cannot be computed or operated as Bayesian update. Operational cessation.
Relations to this entry
- predictive-distribution← DEPENDS_ON
Predictive distribution is defined as marginalizing likelihood p(x_new|θ) over posterior p(θ|x). Removing the posterior removes the integration kernel; the predictive distribution cannot be computed or operated as a Bayesian forecast. Operational cessation, not conceptual sayability.
Record identity
- Created
- Sep 4, 2026, 8:30 AM UTC
- Content hash
- afa013f32993d0c6b1518e9516a1ce1c424ef28f9a2c039ee0ca4eb2763d3fc5