Copula based factorization in Bayesian multivariate infinite mixture models

Martin Burda () and Artem Prokhorov

Journal of Multivariate Analysis, 2014, vol. 127, issue C, 200-213

Abstract: Bayesian nonparametric models based on infinite mixtures of density kernels have been recently gaining in popularity due to their flexibility and feasibility of implementation even in complicated modeling scenarios. However, these models have been rarely applied in more than one dimension. Indeed, implementation in the multivariate case is inherently difficult due to the rapidly increasing number of parameters needed to characterize the joint dependence structure accurately. In this paper, we propose a factorization scheme of multivariate dependence structures based on the copula modeling framework, whereby each marginal dimension in the mixing parameter space is modeled separately and the marginals are then linked by a nonparametric random copula function. Specifically, we consider nonparametric univariate Gaussian mixtures for the marginals and a multivariate random Bernstein polynomial copula for the link function, under the Dirichlet process prior. We show that in a multivariate setting this scheme leads to an improvement in the precision of a density estimate relative to the commonly used multivariate Gaussian mixture. We derive weak posterior consistency of the copula-based mixing scheme for general kernel types under high-level conditions, and strong posterior consistency for the specific Bernstein–Gaussian mixture model.

Keywords: Nonparametric copula; Nonparametric consistency; Mixture modeling (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X14000347
Full text for ScienceDirect subscribers only

Related works:
Working Paper: Copula Based Factorization in Bayesian Multivariate Infinite Mixture Models (2012)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:127:y:2014:i:c:p:200-213

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2014.02.011

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().