Disease Test: In this classic example of Bayes' theorem for discrete events, one would like to determine the posterior probability of the patient having the disease, given that they test positive, which turns out to be a function of prevalence, sensitivity and specificity.
It is commonplace to extend Bayes' theorem to functions for the prior, likelihood, posterior and indeed the evidence, not least in order to enable propagation of uncertainties on the input parameters, and then to use sampling e.g. MCMC, nested sampling etc. to solve for the full posterior.
Q. What form of the likelihood function should one adopt? What would be candidates for the prior distribution?