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Bayesian Theory and Applications$
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Paul Damien, Petros Dellaportas, Nicholas G. Polson, and David A. Stephens

Print publication date: 2013

Print ISBN-13: 9780199695607

Published to Oxford Scholarship Online: May 2013

DOI: 10.1093/acprof:oso/9780199695607.001.0001

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Revisiting Bayesian curve fitting using multivariate normal mixtures ∗

Revisiting Bayesian curve fitting using multivariate normal mixtures ∗

Chapter:
(p.297) 15 Revisiting Bayesian curve fitting using multivariate normal mixtures
Source:
Bayesian Theory and Applications
Author(s):

Stephen G Walker

George Karabatsos

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199695607.003.0015

This chapter develops a Bayesian nonparametric regression model which relies on a standard Bayesian nonparametric form for the joint distribution of both the dependent and independent variables. The regression model then is available as a conditional density which can only be written as a ratio of two infinite-dimensional mixture models. The chapter is organized as follows. Section 15.2 describes the regression model and the methods for sampling the posterior distribution of the model. To obtain full posterior inference of the model, a reversible-jump sampling algorithm is used to deal with the uncomputable normalizing constant. Section 15.3 illustrates the model using data analysis.

Keywords:   Bayesian nonparametric regression model, conditional density, mixture models

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