ABSTRACT
Bayesian statistics is based on Bayes’ rule, which is named after the Rev. Thomas Bayes, who discussed it in a paper published posthumously in 1763. The simple example illustrates two very important aspects of Bayesian analysis. The first is that in order to compute the posterior density one must compute the marginal density by evaluating an integral. The second aspect is that in this example the posterior density has the same form as the prior; both are normal. This is a very special and convenient property of the normal density. It means that if a second measurement is made, the posterior just computed can serve as the prior for a second calculation. The availability of inexpensive, powerful computers beginning in the 1980s motivated the development of numerical methods that eliminate the need to restrict Bayesian analysis to likelihood functions that are associated with conjugate priors.
