Bayesian methods are grounded in a very different conceptual framework and are becoming more popular in genetic epidemiology [67]. The principle of Bayesian tests of association is to first assume prior probabilities on the two hypotheses of no association and association, then use the data to update the prior probabilities of the two hypotheses into their posterior probabilities. The decision to reject the null hypothesis is then based on appropriate thresholds on the odds of the posterior probabilities or, equivalently, on the posterior probability of the null hypothesis. The choice of the best threshold can be based on trading off sensitivity and specificity of the Bayesian decision rule (see Fig. 4 for an example). The posterior odds are computed by multiplying the prior odds by the Bayes factor that can be calculated in closed form for some of the models described earlier [65]. Nonlinear models usually require sophisticated computational procedures and stochastic computations known as Markov Chain Monte Carlo methods [67]. These methods are very powerful and are commonly used in genetics as they are the engine of very accurate
