Some issues in nonparametric Bayesian modelling using species sampling models
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Date
2008
Journal Title
Journal ISSN
Volume Title
Publisher
SAGE PUBLICATIONS LTD
Abstract
We review some aspects of nonparametric Bayesian data analysis with discrete random probability measures. We focus on the class of species sampling models (SSMs). We critically investigate the common use of the Dirichlet process (DP) prior as a default SSM choice. We discuss alternative prior specifications from a theoretical, computational and data analysis perspective. We conclude with a recommendation to consider SSM priors beyond the special case of the DP prior, and make specific recommendations on how different choices can be used to reflect prior information and how they impact the desired inference. We show the required changes in the posterior simulation schemes, and argue that the additional generality can be achieved without additional computational effort.
Description
Keywords
density estimation, Pitman-Yor process, random probability measures, DIRICHLET PROCESS MIXTURE, POLYA TREE DISTRIBUTIONS, CHAIN MONTE-CARLO, GAMMA PROCESSES, DENSITY-ESTIMATION, BINARY SEQUENCES, UNKNOWN NUMBER, COUNT DATA, INFERENCE, BETA