I'm reviewing Bayes' theorem and related topics for the upcoming GDAT class. In its simplest form, Bayes' theorem is statement about conditional probabilities. The probability of A, given that B has occurred, is expressed as: \begin{equation} \Pr(A|B) = \dfrac{\Pr(B|A)\times\Pr(A)}{\Pr(B)} \label{eqn:bayes} \end{equation} In Bayesian language, $\Pr(A|B)$ is called the posterior probability, $\Pr(A)$ the prior probability, and $\Pr(B|A)$ the...