Seminario del prof. Fabio Divino (Division of Physics Computer Science and Mathematics, University of Molise, Italy)
Abstract
In this talk some preliminary results in Bayesian inference of multivariate discrete distributions are presented. In particular, an empirical Bayesian approach is considered through the use of the Dirichlet-Multinomial compound model. The idea of compound models is back to the beginning of the 1900 and it concerns the possibility to compound a model of interest M0(X;T), depending on some parameter T, with a mixing probability measure Ha(T) on T, depending on a parameter a. In this way, the mixture resulting by the integration of M0 respect to Ha generates a new model M1(X; a) that allows for the possibility of including larger variation for the variable X than in M0. A typical application of this approach is the well known Gamma-Poisson compound model that generates the Negative Binomial model. In this talk we present the use of the Dirichlet-Multinomial model in order to estimate the probability distribution of an overdispersed multivariate discrete random variable X. Some results of simulations will compare the Dirichlet-Multinomial model with the reference Multinomial model. Further, some applications in biodiversity monitoring will be presented.
The work is part of a joint research with Salme Kärkkäinen, Johanna Ärje and Antti Penttinen (University of Jyväskylä) and Kristian Meissner (SYKE, Jyväskylä).