Statistics of Copulas

This chapter contains the general discussion of the most logical criteria of quality of statistical models helpful in choosing one copula model over another one. The difference between Bayesian and classical methods consists in more than just the difference between two point estimators: say, maximum likelihood estimator versus the posterior mean incorporating some prior information. The most important aspect of Bayesian estimation is that the inference gives us entire posterior distribution rather than one point estimate. Bayesian statistics plays an important role in Bayesian estimation to find the best solutions in the subclasses of copulas, and also Bayesian hypothesis testing for the purpose of model selection between these subclasses. The chapter considers Bayesian copula estimation for a joint survival problem and Bayesian model selection for the related failures of vehicle components.