Applied Math Seminar: SIMULATION FROM A NORMALLY WEIGHTED DIRICHLET DISTRIBUTION
3:10 PM, Neill 3W
Abstract: Analysis of a class of non-neutral population genetics models requires the simulation of samples, computation of sample statistics, and 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 fast and accurate computation of the normalizing constant for the distribution function. The method relies on a sequence of convolutions that can be efficiently computed using fast Fourier transforms. The result of these computations is a set of approximate marginal distribution functions for the original density. These distribution functions can then be used to efficiently compute samples from the multivariate distribution.