Bayesian Credible Interval
Definition
An interval computed from the posterior distribution of a parameter, given a prior and the observed data. Unlike a confidence interval, a credible interval carries a direct probability statement: there is a stated probability that the parameter lies in the interval.
- Field
- Bayesian statistics
- Computed from
- Posterior distribution
- Interpretation
- Direct probability the parameter lies in the interval
- Contrast
- Differs from a frequentist confidence interval
Common questions
Why is a credible interval easier to explain to a jury than a confidence interval?+
A credible interval supports the direct statement that there is a given probability the true value falls within the range, which matches how most people intuitively want to interpret an interval, whereas a confidence interval technically describes the long-run behaviour of the interval-construction procedure, not the parameter itself.
Does a credible interval depend on the choice of prior?+
Yes. Because it is derived from the posterior distribution, which combines the prior with the observed data, a different reasonable prior can shift the interval, so the prior used should be stated and justified alongside the interval itself.
Related terms
- Confidence Interval (CI)
- A range computed from sample data using a procedure that, over many repetitions, would contain the true population parameter a stated percentage...
- Coverage Probability
- The true long-run proportion of intervals, from repeated sampling, that contain the parameter. If a procedure has 95% nominal coverage and its...
- Critical Value
- The value from a reference distribution (z or t) that cuts off the desired tail probability. For a 95% two-sided interval using...
- Margin of Error
- Half the width of a symmetric confidence interval, equal to the critical value multiplied by the standard error. Commonly reported in survey...
- Standard Error (SE)
- The standard deviation of the sampling distribution of an estimator. For the sample mean, SE equals the population standard deviation divided by...