A0375
Title: Dependent Dirichlet-multinomial processes with random number of components
Authors: Andrea Cremaschi - IE University (Spain) [presenting]
Beatrice Franzolini - Bocconi University (Italy)
Abstract: Bayesian nonparametric methods under partial exchangeability have largely focused on infinite support priors, yet almost-surely finite dimensional dependent mixtures remain underexplored despite their strong theoretical guarantees and performance in the exchangeable case. A novel class of finite dependent Dirichlet-multinomial processes and their counterparts are introduced, incorporating a prior on the number of components. The class is built on generalized Wishart unnormalized weights. It is proven that the normalized diagonals of correlated Wishart matrices admit a hierarchical negative binomial Dirichlet representation whose marginal laws are Dirichlet. The key distributional properties of the induced random probability measures are derived, showing they can achieve any prescribed dependence level and support efficient posterior computation without the need for costly variable augmentation schemes. The practical advantages of the proposed processes are further demonstrated through extensive simulation studies and the analysis of two real datasets: A benchmark dataset and a case study on sex-specific gene expression differences in the human brain, highlighting its flexibility and computational efficiency in capturing complex dependence structures.
