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In this paper, we discuss the construction of a multivariate generalisationof the Dirichlet-multinomial distribution. An example from forensic genetics inthe statistical analysis of DNA mixtures motivates the study of thismultivariate extension.  In forensic genetics, adjustment of the match probabilities due to remoteancestry in the population is often done using the so-called{\theta}-correction. This correction increases the probability of observingmultiple copies of rare alleles and thereby reduces the weight of the evidencefor rare genotypes.  By numerical examples, we show how the {\theta}-correction incorporated bythe use of the multivariate Dirichlet-multinomial distribution affects theweight of evidence. Furthermore, we demonstrate how the {\theta}-correction canbe incorporated in a Markov structure needed to make efficient computations ina Bayesian network.

The multivariate Dirichlet-multinomial distribution and its application  in forensic genetics to adjust for sub-population effects using the  {\theta}-correction