A copula is a multivariate model whose marginals are uniform. A copula based model is one that is based on a copula. The attraction of using copula models is that we can separately model the marginal distributions and the dependence structure of our target distribution. Such models are particularly attractive when some or all of the marginals are discrete or a mixture of discrete and continuous components. A multivariate probit model is one simple example of a copula model.
The aim of this project is to develop flexible methods for building copula based models. We have three working papers on this project.
1) This paper develops a pseudo marginal method for estimating high dimensional copulas. Title: Computationally Efficient Bayesian Estimation of High Dimensional Copulas with Discrete and Mixed Margins. authors: D. Gunawan, M.-N. Tran, K. Suzuki, J. Dick, R. Kohn. address: https://arxiv.org/abs/1608.06174
2) This paper shows how to constructor a universal approximator to a copula. It has the same motivation as using a mixture of multivariate normals to construct a universal approximator to any multivariate distribution. Title: The Approximation Properties of Copulas by Mixtures. Authors: Mohamad A. Khaled, Robert Kohn. Address: https://arxiv.org/abs/1705.10440
3) This paper shows how to estimate a copula each of whose margins can be a mixture of discrete and continuous components. Title: Mixed Marginal Copula Modeling. David Gunawan, Mohamad A. Khaled, Robert Kohn. Address: https://arxiv.org/abs/1605.09101