JSM 2004 - Toronto

Abstract #300725

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Activity Number: 147
Type: Topic Contributed
Date/Time: Monday, August 9, 2004 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #300725
Title: Random Probability Measures Derived from Increasing Additive Processes and Their Application to Bayesian Statistics
Author(s): Igor Pruenster*+
Companies: University of Pavia
Address: Dip. to di Economia Politica e Metodi Quantitativi, Pavia, International, 27100, Italy
Keywords: Bayesian nonparametrics ; Dirichlet process ; increasing additive process ; neutral to the right process ; normalized random measure
Abstract:

Increasing additive processes (IAP), i.e. processes with non-negative independent increments, represent a natural tool for defining random probability measures whose distributions act as nonparametric priors for Bayesian inference. It is well known that the Dirichlet process can be obtained either by normalizing a time-changed gamma process or, as a particular case of neutral to the right process, by the exponential transformation of a suitable IAP. The former construction is generalized to any IAP yielding the class of normalized random measures with independent increments (normalized RMI). Simple rules for the prior specification of normalized RMI and expressions for their posterior and predictive distributions are obtained. Moreover, results concerning the distribution of their means are provided. Due to their potential relevance in applications, normalized inverse Gaussian processes are considered in detail. Normalized RMI are then further generalized to normalized IAP driven random measures, which contain the mixture of Dirichlet process as a particular case. Finally, means of neutral to the right processes are studied.

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