Approximate Bayesian Computation for Copula Estimation

We describe a simple method for making inference on a functional of a multivariate distribution. The method is based on a copula representation of the multivariate distribution and it is based on the properties of an Approximate Bayesian Monte\,Carlo algorithm, where the proposed values of the functional of interest are weighed in terms of their empirical likelihood. This method is particularly useful when the 'true' likelihood function associated with the working model is too costly to evaluate or when the working model is only partially specified.

[2]  S. Walker,et al.  Bayesian Nonparametric Inference for a Multivariate Copula Function , 2014 .

[3]  C. Czado,et al.  Bayesian inference for multivariate copulas using pair-copula constructions. , 2010 .

[4]  C. Genest,et al.  A semiparametric estimation procedure of dependence parameters in multivariate families of distributions , 1995 .

[5]  E. Luciano,et al.  Copula methods in finance , 2004 .

[6]  Radu V. Craiu,et al.  In mixed company: Bayesian inference for bivariate conditional copula models with discrete and continuous outcomes , 2012, J. Multivar. Anal..

[7]  M. Sklar.  Fonctions de repartition a n dimensions et leurs marges , 1959 .

[8]  Peter D. Hoff.  Extending the rank likelihood for semiparametric copula estimation , 2006, math/0610413.

[9]  S. Sisson,et al.  Likelihood-free Markov chain Monte Carlo , 2010, 1001.2058.

[10]  J. Geweke,et al.  Bayesian Treatment of the Independent Student- t Linear Model , 1993 .

[11]  R. Kohn,et al.  Modeling Dependence Using Skew T Copulas: Bayesian Inference and Applications , 2010 .

[12]  Christian P Robert,et al.  Bayesian computation via empirical likelihood , 2012, Proceedings of the National Academy of Sciences.

[13]  M. Smith.  Bayesian Approaches to Copula Modelling , 2011, 1112.4204.

[14]  T. Gneiting,et al.  Uncertainty Quantification in Complex Simulation Models Using Ensemble Copula Coupling , 2013, 1302.7149.

[15]  Dong Hwan Oh,et al.  Simulated Method of Moments Estimation for Copula-Based Multivariate Models , 2013 .

[16]  Susanne M. Schennach,et al.  Bayesian exponentially tilted empirical likelihood , 2005 .

[17]  C. Genest,et al.  Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask , 2007 .

[18]  Yanan Fan,et al.  Likelihood-Free MCMC , 2011 .

[19]  Hongzhe Li,et al.  A Gaussian copula approach for the analysis of secondary phenotypes in case-control genetic association studies. , 2012, Biostatistics.

[20]  H. Joe.  Dependence Modeling with Copulas , 2014 .

[21]  Xiaotong Shen,et al.  Empirical Likelihood , 2002 .

[22]  Jean-Michel Marin,et al.  Approximate Bayesian computational methods , 2011, Statistics and Computing.

[23]  Hedibert Freitas Lopes,et al.  Copula, marginal distributions and model selection: a Bayesian note , 2008, Stat. Comput..

[24]  P. Friederichs,et al.  Multivariate non-normally distributed random variables in climate research - introduction to the copula approach , 2008 .

[25]  D. Rubin.  Using the SIR algorithm to simulate posterior distributions , 1988 .

[26]  Pierre Chauss,et al.  Computing Generalized Method of Moments and Generalized Empirical Likelihood with R , 2010 .

[27]  Lennart F. Hoogerheide,et al.  Bayesian Estimation of the GARCH(1,1) Model with Student-t Innovations , 2009, R J..