Bayes’ Theorem

In this chapter, we describe the history and development of Bayes’ theorem, and report on several applications Bayesian theory has had on innumerable scientific and non-scientific endeavours. We introduce Bayesian theory as a fundamental tool for updating probabilities based on new evidence, explaining its relevance in making well-informed decisions in clinical practice. We present the basic mathematical premise behind this theory, and derive the screening equation—also known as the expanded Bayesian equation, from the basic form of the theorem. Provided the sensitivity and specificity of a screening test are known, the screening equation allows for the calculation of the positive predictive value, \(\rho (\phi )\) , as a function of disease prevalence or pretest probability, \(\phi \) .