Bayesian uncertainty

• Frequentists assess uncertainty with confidence intervals, whereas Bayesians calculate posterior distributions and credible intervals.

• The Bayesian posterior distribution tells us how likely specific parameter estimates are given the input data. The credible interval indicates a range of values in which the parameter value is expected with a given probability, as calculated from the posterior distribution. For example, a 95% credible interval corresponds to the center 95% of the posterior distribution. The true parameter value has a 95% chance of lying in the 95% credible interval.

• A Bayesian credible interval makes a statement about the true parameter value and a frequentist confidence interval makes a statement about the null hypothesis.