Statistical Modelling 8 (2008), 3–21
Some issues in nonparametric Bayesian modeling using species sampling models
Carlos Navarrete
Departamento de Matemática, Universidad del Bío Bío,
Chile
Fernando A Quintana
Departamento de Estadística,
Pontificia Universidad Católica de Chile,
Avenida V Mackenna 4860,
Santiago
eMail:
quintana@mat.puc.cl
Peter Müller
Department of Biostatistics and Applied Mathematics,
The University of Texas,
USA
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.
Keywords:
density estimation; Pitman–Yor process; random probability measures
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