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Title: Bayesian semiparametric copula estimation using an infinite mixture of Gaussian copulas. Authors:  Jichan Park - Korea University (Korea, South) [presenting]
Taeryon Choi - Korea University (Korea, South)
Abstract: A Bayesian semiparametric approach is presented for estimating an unknown bivariate copula using an infinite mixture of Gaussian copulas. To accomplish this, we use a copula model that can separately build the dependence structure and marginal distributions of a bivariate distribution. The dependence structure is induced by different parametric bivariate copulas such as Gaussian, Student $t$, Clayton and Gumbel copula and specifically, they are sampled through the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm. Furthermore, we consider Dirichlet process priors to estimate a more flexible dependence structure in the nonparametric way. Marginal distributions are estimated via the Bayesian spectral analysis density estimation (BSAD) method with and without shape restrictions. Finally, we study the performance of the RJMCMC algorithm and compare estimates in each model with simulations of various settings and several real data sets.