A new approximation of the posterior distribution of the log–odds ratio

In this paper, the posterior density of the log–odds ratio is studied. It is assumed that the observations have a multinomial distribution and that the prior on the multinomial parameters is a Dirichlet density. Several approximations currently available are reviewed. Under certain conditions on the prior parameters of the Dirichlet density, it is shown that the posterior moments can be computed exactly. A new approximation, similar to the Edgeworth expansion is also proposed. Using a numerical example, the different methods of approximation of posterior density are compared.