95% Credible Intervals

The 95% Credible Interval (abbreviated as 95% CrI) defines the range in which the model is 95% certain that the true value lies.

The 95% CrI has this interpretation because it contains 95% of the probability mass of the entire posterior distribution. And not just any 95%: it contains the highest-density 95% (i.e., the “tallest” and “narrowest” region possible).

Put differently, the 95% CrI spans the distribution from the 2.5th quantile up to the 97.5th quantile.

Here’s how it looks, shaded in light blue:

The interpretation of the Bayesian Credible Interval—the range within which, with 95% probability, the true value lies—is the interpretation we often instinctively want the frequentist confidence interval to have.

This is considered by some to be a point in favour of the Bayesian framework: it reflects our intuitions a little bit better.