Posterior analysis for some classes of nonparametric models

Authors: Lijoi, Antonio¹; Prunster, Igor²; Walker, S. G.³

Source: Journal of Nonparametric Statistics, Volume 20, Number 5, July 2008 , pp. 447-457(11)

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Abstract:

Recently, James [L.F. James, Bayesian Poisson process partition calculus with an application to Bayesian Levy moving averages, Ann. Statist. 33 (2005), pp. 1771-1799.] and [L.F. James, Poisson calculus for spatial neutral to the right processes, Ann. Statist. 34 (2006), pp. 416-440.] has derived important results for various models in Bayesian nonparametric inference. In particular, in ref. [L.F. James, Poisson calculus for spatial neutral to the right processes, Ann. Statist. 34 (2006), pp. 416-440.] a spatial version of neutral to the right processes is defined and their posterior distribution derived. Moreover, in ref. [L.F. James, Bayesian Poisson process partition calculus with an application to Bayesian Levy moving averages, Ann. Statist. 33 (2005), pp. 1771-1799.] the posterior distribution for an intensity or hazard rate modelled as a mixture under a general multiplicative intensity model is obtained. His proofs rely on the so-called Bayesian Poisson partition calculus. Here we provide alternative proofs based on a different technique.

Keywords: Bayesian nonparametrics; completely random measure; hazard rate; multiplicative intensity model; neutral to the right prior

Document Type: Research article

DOI: http://dx.doi.org/10.1080/10485250802196364

Affiliations: 1: Dipartimento di Economia Politica e Metodi Quantitativi, Universita degli Studi di Pavia, Pavia, Italy,CNR-IMATI, Milano, Italy 2: Dipartimento di Statistica e Matematica Applicata, Collegio Carlo Alberto and ICER, Universita, Torino, Italy 3: Institute of Mathematics, Statistics and Actuarial Science, University of Kent, Kent, UK

Publication date: 2008-07-01