Copula Based Factorization in Bayesian Multivariate Infinite Mixture Models

Martin Burda () and Artem Prokhorov

Working Papers from University of Toronto, Department of Economics

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. In economics, they have been particularly useful in estimating nonparametric distributions of latent variables. However, these models have been rarely applied in more than one dimension. Indeed, the multivariate case suffers from the curse of dimensionality, with a rapidly increasing number of parameters needed to jointly characterize each mixing component. In this paper, we propose a factorization scheme for nonparametric mixture models whereby each marginal dimension in the mixing parameter space is modeled separately, 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 Dirichlet process priors. We show that this scheme leads to an improvement in the precision of a density estimate in finite samples, providing a suitable tool for applications in higher dimensions. 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)
JEL-codes: C11 C14 C63 (search for similar items in EconPapers)
Pages: Unknown pages
Date: 2013-01-28
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Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Copula based factorization in Bayesian multivariate infinite mixture models (2014)
Working Paper: Copula Based Factorization in Bayesian Multivariate Infinite Mixture Models (2012)
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