---
tag: 441PZ3T7F0
kind: concept
name: Credible interval
msc: [62F15, 62F25]
sources:
  - url: https://en.wikipedia.org/wiki/Credible_interval
same_as:
  wikidata: Q4439221
  wikipedia: Credible interval
---

## Summary

A credible interval is an interval of parameter values that has a given probability, such as $95\%$, under the [[posterior distribution|0KJ7ZS8AJA]].
It is the Bayesian counterpart of a [[confidence interval|0S6T9KQNC0]].
Its probability statement is about the parameter given the observed data, which is how confidence intervals are often, wrongly, read.

## Explanations

### L1 human

After seeing the data, a Bayesian has a probability distribution for the unknown quantity.
A $95\%$ credible interval is a range that holds $95\%$ of this probability.
So one may say "given the data and the prior, the parameter lies in this range with probability $95\%$".
For example, if the posterior of a mean is normal with mean $10$ and standard deviation $1$, then $[8.04, 11.96]$ is a $95\%$ credible interval.