Improper prior
Topic of Bayesian foundations, part of Bayesian statistics
Improper prior
| Type | Topic |
| Taught in | Bayesian foundations |
| Part | Bayesian statistics |
| Questions using it | 4 |
A prior density whose integral is infinite, such as a flat density on the whole real line. It is not a probability distribution, and it is usable only when the posterior it produces is proper, which has to be checked rather than assumed.
In Bayesian foundations
From Bayesian foundations
A prior is proper if it is a probability distribution, so its total mass is one. A posterior is proper if the product of likelihood and prior has a finite, nonzero normalising constant. An improper prior may sometimes produce a proper posterior, but this must be checked rather than assumed.
Used in
- Taught in Bayesian foundations
- Also used in Exponential families and conjugacy · Hierarchical Bayes
- Questions that use it (4) — Bayesian regression and prediction (answer) · Unknown Normal mean and variance: conditional versus marginal (answer) · Improper prior for a normal sample (answer) · Bayesian model selection
- All 15 questions on Bayesian foundations
See also
Proper prior and proper posterior · Bayesian credible interval · Bayes’ rule · Posterior point summaries · Credible-region constructions · Posterior summaries from draws · R’s distribution interface · Prior and posterior predictive distributions