Bayesian Statistics

Bayesian statistics is a comprehensive and systematic interpretation of the field of statistics based on the quantification and manipulation of uncertainty in the form of probability distributions enabled by the Bayesian interpretation of probability laws. It is commonly considered a branch of statistics. This entry provides a basic description of Bayesian statistics. Although Bayesian statistics includes nonparametric approaches, the entry’s scope is limited to the more common setting of parametric Bayesian inference.

[Page 171]Although the historical details surrounding the origins of Bayesian statistics are somewhat hazy, the broad strokes are well-documented. The basic theoretical machinery underpinning Bayesian statistics was established in the second half of the 18th century with the discovery of Bayes’s theorem by Thomas Bayes, Richard Price, and, independently, Pierre-Simon Laplace. If beliefs concerning ...