Griffin, Jim E. and Steel, Mark F. J.. (2006) Order-based dependent Dirichlet processes. Journal of the American Statistical Association, Vol.101 (No.473). pp. 179-194. ISSN 0162-1459

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Abstract

In this article we propose a new framework for Bayesian nonparametric modeling with continuous covariates. In particular. we allow the nonparametric distribution to depend on covariates through ordering the random variables building the weights in the stick-breaking representation. We focus mostly on the class of random distributions that induces a Dirichlet process at each covariate value. We derive the correlation between distributions at different covariate values and use a point process to implement a practically useful type of ordering, Two main constructions with analytically known correlation structures are proposed. Practical and efficient computational methods are introduced. We apply our framework, through mixtures of these processes, to regression modeling, the modeling of stochastic volatility in time series data, and spatial geostatistical modeling.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Journal or Publication Title:	Journal of the American Statistical Association
Publisher:	American Statistical Association
ISSN:	0162-1459
Date:	March 2006
Volume:	Vol.101
Number:	No.473
Number of Pages:	16
Page Range:	pp. 179-194
Identification Number:	10.1198/016214505000000727
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/33789

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