Normalized random measures driven by increasing additive processes

Luis E. Nieto-Barajas, Igor Prünster, Stephen G. Walker

The Annals of Statistics · 2004 · Volume 32 · Issue 6

Abstract

This paper introduces and studies a new class of nonparametric prior distributions. Random probability distribution functions are constructed via normalization of random measures driven by increasing additive processes. In particular, we present results for the distribution of means under both prior and posterior conditions and, via the use of strategic latent variables, undertake a full Bayesian analysis. Our class of priors includes the well-known and widely used mixture of a Dirichlet process.

Keywords

60G57, 62F15, Bayesian nonparametric inference, distribution of means of random probability measures, increasing additive process, Lévy measure, mixtures of Dirichlet process

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