Bayesian Credible Intervals

A 95% Bayesian credible interval is the range within which the parameter lies with 95% posterior probability. This is a direct probability statement: 'Given the data and prior, there is a 95% probability that the true parameter falls in this interval.' Compare this to a 95% confidence interval, which means: 'If we repeated this procedure many times, 95% of intervals would contain the true parameter.' The confidence interval says nothing about any specific interval—it describes the long-run behavior of the procedure. Most people naturally interpret confidence intervals as credible intervals (a direct probability statement), which is why Bayesian credible intervals align better with intuitive reasoning.