Credible interval

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In Bayesian statistics, a credible interval is a posterior probability interval, used for purposes similar to those of confidence intervals in frequentist statistics.

For example, a statement such as "following the experiment, a 90% credible interval for the parameter t is 35-45" means that the posterior probability that t lies in the interval from 35 to 45 is 0.9.

There are several ways of constructing credible intervals from a given probability distribution for the parameter. Examples include:

• choosing the narrowest interval, which for a unimodal distribution will involve choosing those values of highest probability density including the mode.
• choosing the interval where the probability of being below the interval is as likely as being above it; the interval will include the median.
• choosing the interval which has the mean as its central point.

[edit] Distinction between a Bayesian credible interval and a frequentist confidence interval

By contrast, a frequentist confidence interval (e.g. a 90% confidence interval of 35-45) means that with a large number of repeated samples, 90% of the calculated confidence intervals would include the true value of the parameter. The probability that the parameter is inside the given interval (say, 35-45) is either 0 or 1 (the non-random unknown parameter is either there or not). In frequentist terms, the parameter is fixed (cannot be considered to have a distribution of possible values) and the confidence interval is random (as it depends on the random sample).

Since many non-statisticians intuitively interpret confidence intervals in the Bayesian credible interval sense, "credible intervals" are sometimes called "confidence intervals".