Sergio Bacallado

Center for the Mathematical Sciences, University of Cambridge

Unbiased estimation and prediction in the hierarchical two-parameter Poisson-Dirichlet process

Statistics Seminar

27th October 2017, 2:00 pm – 3:00 pm
Main Maths Building, SM3

Bayesian nonparametric modelling of partially exchangeable sequences requires prior distributions on dependent random measures. A common choice is to let the random measures be conditionally independent given a latent discrete distribution. Such models give rise to natural urn schemes for sampling the prior distribution. On the other hand, posterior inference most often requires Markov chain Monte Carlo techniques. We propose an exact sampler for latent variables which allows exact sampling from the predictive distribution in the hierarchical two-parameter Poisson-Dirichlet process, a flexible family of dependent random measures. We also study the performance of debiasing methods proposed by Rhee and Glynn for the same class of models. Experiments show that the Markov chain samplers considered mix very slowly in certain regions of parameter space, displaying a sharp transition.

Organiser: Henry Reeve

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