In praise of Bayes

Bayesian inference is the most comprehensive alternative paradigm to frequentist methods of statistical inference. It owes its beginnings to work carried out by the Reverend Thomas Bayes in the mid‐eighteenth century. Frequentist inference has very limited ways of accommodating ‘fuzzy’ prior information in interval estimation and hypothesis testing, and can do so only if the fuzziness of that prior information is measured by an objective probability. Bayesian inference, by contrast, makes it easy to incorporate fuzzy prior information even when the fuzziness is gauged by a subjective probability. Even better, Bayesian inference provides for the possible updating of an initial subjective probability using new objective probability information, as it becomes available. The mechanism for doing this updating is Bayes’ theorem. Bayesian inference has had many spectacular successes in important inferential contexts.