Title: Bayesian inference for finite-dimensional discrete priors
Authors: Tommaso Rigon - Bocconi University (Italy) [presenting]
Antonio Lijoi - Bocconi University (Italy)
Igor Pruenster - Bocconi University (Italy)
Abstract: Discrete random probability measures are the main ingredient for addressing Bayesian clustering. The investigation in this area has been very lively, with strong emphasis on nonparametric procedures based either on the Dirichlet process or on more flexible generalizations, such as the Pitman-Yor (PY) process or the normalized random measures with independent increments (NRMI). The literature on finite-dimensional discrete priors, beyond the classic Dirichlet-multinomial model, is much more limited. We aim at filling this gap by introducing novel classes of priors closely related to the PY process and NRMIs, which are recovered as limiting case. Prior and posterior distributional properties are extensively studied. Specifically, we identify the induced random partitions and determine explicit expressions of the associated urn schemes and of the posterior distributions. A detailed comparison with the (infinite-dimensional) PY and NRMIs is provided. Finally, we employ our proposal for mixture modeling, and we assess its performance over existing methods in the analysis of a real dataset.