Bayes Theorem: Computing the Posterior Distribution
Emmanuel M. E. H. Lesaffre, Andrew B Lawson · 2012
This chapter derives the general Bayes theorem and illustrates it with a variety of examples. Comparisons of the Bayesian solution with the frequentist and the likelihood solution is made for a better understanding of the Bayesian concepts. In fact, inference turns out to be quite different from the classical case, even probability will get a different flavor in the Bayesian paradigm. The chapter discusses the mechanics of Bayes theorem in more detail. Three cases are exemplified: the binomial, the normal and the Poisson case. The binomial likelihood combined with a beta prior produces a beta posterior. A similar conjugacy property holds in the Gaussian case, since a normal likelihood combined with a normal prior gives a normal posterior. Further, the chapter illustrates the impact of choosing different priors on the posterior distribution and indicated that the prior is the cause of much of the controversy around the Bayesian paradigm. Controlled Vocabulary Terms Bayes’ theorem; Gaussian process; Poisson distribution