Calculation of maximum entropy distributions and approximation of marginalposterior distributions

It is shown how members of the broad class of Cobb-Koppstein-Chen probability density functions can be generated by maximizing Shannon's entropy subject to appropriate side conditions. A particular member of the class, the quartic exponential distribution, is obtained by maximizing Shannon's entropy subject to the conditions that the probability density function integrate to one and have given first four moments. An algorithm for computing the quartic exponential distribution is provided and applied to approximate marginal posterior probability densities. These approximations are compared with those provided by the Pearson density function approximation procedure and exact densities obtained by numerical integration. It is found that the maximum entropy method performs very well.