A predictive distribution is the probability distribution p(x_new|x) over new or future data x_new, given observed data x, computed by marginalizing the likelihood p(x_new|θ) over the posterior distribution p(θ|x): p(x_new|x) = ∫ p(x_new|θ) p(θ|x) dθ. Its parameters are the observed data (which determines the posterior), the model's likelihood function, and the parameter space. It persists as the canonical Bayesian forecasting tool, encoding both epistemic uncertainty (via the posterior) and aleatoric uncertainty (via the likelihood), and is used for out-of-sample prediction, model comparison via marginal likelihood, and Bayesian model averaging. [formal: predictive distribution | substrate: mind | horizon: a life | explicit: yes | epoch: 0.01]
Accepted ontology entry
predictive-distribution
A predictive distribution is the probability distribution p(x_new|x) over new or future data x_new, given observed data x, computed by marginalizing the likelihood p(x_new|θ) over the posterior distribution p(θ|x): p(x_new|x) = ∫ p(x_new|θ…
Definition
Why it is in scope
A human-made probability distribution over future or unobserved data, marginalized over the posterior distribution of model parameters. It is the canonical Bayesian tool for out-of-sample prediction, built to persist as the standard probabilistic forecast in Bayesian analysis.
Names and aliases
- predictive-distributionen · CANONICAL
Relations from this entry
- posterior-distributionDEPENDS_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.
- cmsm3b2kp00c51q13zu38aip0DEPENDS_ON →
Predictive distribution is the canonical Bayesian forecasting tool. Remove Bayesian inference framework and predictive distribution has no operational definition. Law 8b removal test satisfied.
- likelihood-functionDEPENDS_ON →
Predictive-distribution computes the probability of new data by integrating over parameter uncertainty, marginalizing the likelihood-function against the posterior. Remove the likelihood-function and predictive-distribution has no data-model to predict from — constitutive dependency per Law 8.
Relations to this entry
No accepted relations in this direction.
Record identity
- Created
- Sep 4, 2026, 8:30 AM UTC
- Content hash
- 1bda9b9791df923043b83dc5909a956e43bbd6c143869b564b175ea3390af0ed