Title: Efficient Gibbs sampling methods for hierarchical processes
Authors: Tommaso Rigon - Bocconi University (Italy) [presenting]
Antonio Lijoi - Bocconi University (Italy)
Igor Pruenster - Bocconi University (Italy)
Abstract: Within a Bayesian nonparametric framework, there is an increasing interest in flexibly learning how the distribution of a response variable changes across groups of observations. Popular models in such a setting are the hierarchical Dirichlet process and the wider class of hierarchical normalized random measures. The latter provides additional modeling flexibility, for instance because it allows for a deeper control of the underlying clustering mechanism. This obviously comes at a higher computational cost: posterior inference, although theoretically possible, might be cumbersome in practice. We aim to fill this gap by proposing an approximation for a general class of hierarchical processes, which leads to a straightforward Gibbs sampling algorithm. To this purpose, we employed a deterministic truncation of the involved random probability measures, obtaining a finite dimensional approximation of the original prior law. We provide both empirical and theoretical support for such a truncation. Our proposal is assessed through simulation studies and finally employed in an illustrative analysis.