LA DISTRIBUZIONE A POSTERIORI DELLE SPECIE RARE NEI MODELLI DI CAMPIONAMENTO DI TIPO GIBBS

The study of the posterior distribution of species variety in species sampling models consists in the determination, conditional on an observed sample of size n, of the distribution of the number of species appearing with given frequency in an additional sample of size m. Observations are assumed to be exchangeable and directed by a Gibbs-type prior, a particular class of discrete random probability measures generating an exchangeable partition probability function characterized by product form. Results are then specialized to the case of rare species and to the case of the Poisson-Dirichlet and Dirichlet processes, two examples of Gibbs-type sampling models having good mathematical tractability. Interest in species sampling models is motivated by applied problems involving expensive sampling procedure, where further sampling needs previous estimation of the probability of discovering new species.