Suppose that we have a total of \(m\) possible models with prior probabilities \(g(p), p=\) \(1, \ldots, m\). Show that the posterior probability of model \(g(p \mid \tau)\) can be expressed in terms of all the \(p(p-1)\) Bayes factors:

\[ g(p=i \mid \tau)=\left(1+\sum_{j eq i} \frac{g(p=j)}{g(p=i)} B_{j / i}\right)^{-1} \]