Genz, Alan and Joyce, Paul (2003), Computation of the Normalization Constant for Exponentially Weighted Dirichlet Distribution Integrals, Computing Science and Statistics, 35, I2003Proceedings/GenzAlan/GenzAlan.paper.pdf
Analysis of a class of non-neutral population genetics models requires the simulation of samples, computation of sample statistics and evaluation of likelihood surfaces for a multivariate density function that is the product of a Normal density and a Dirichlet density, defined over an m-dimensional simplex. A method will be described for the accurate computation of the normalizing constant for the distribution function. Several methods will be considered for computing samples from the distribution. The efficiency of the methods will be compared using results from application examples with as many as twenty-five variables.