Bayesian computational statistics

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The Bayesian nonparametric methodology developed in my Ph.D thesis has shown to work well in the context of copula estimation. Although frequentist estimators for the copula function usually have good asymptotic properties, some of them present notable drawbacks for inference using finite samples. The goal of the thesis is to get intrinsic estimators in order to propose a coherent treatment of the uncertainty relative to both, the estimation of the distribution using a finite sample and to the prevision of bivariate data. The idea is first to construct a nonparametric model for the copula functions. The nonparametric nature here means that the number of parameters in the model can be made arbitrarily large. The subspace spanned by the model is then shown to be dense in the space of copulas according to the sup norm. A prior distribution over the set of parameters is selected. The constraints on the parameter space and the complexity of the resulting posterior distribution requires carefully chosen MCMC techniques for inference.