Model Selection as a Prelude of Risk Assessment Studies

In general, model selection is an important prelude to subsequent statistical inference in risk assessment studies, because model misspecication could lead to substantial bias even faulty conclusions. It is well known that the Bayes factor is the most useful tool for model selection and it has been widely applied to a lot of biostatistical problems. Assume that there are two hypotheses H1 and H2 proposed for our interesting data set X; and under Hk, the data are related to the parameter vector k by a distribution with probability density p(X j k; Hk). Given the prior probabilities p(H1) and p(H2) = 1 p(H1), the data produce the posterior probabilities p(H1jX) and p(H2jX) = 1 p(H1jX). From Bayes ' Theorem, we get p(H1jX) p(H2jX) p(X jH1) p(X jH2) p(H1) p(H2) The Bayes factor is dened a