Grant: Discovery Grants Program - Individual

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. The area of research I will primarily concentrate on is in finding new applications and fields which can benefit from this generic methodology. In particular, models will be constructed in the contexts of Archimedean copulas and multivariate extreme value distributions. I will also work in two other fields of Bayesian statistics that are unrelated to my thesis, that is statistical learning with graph-structured data and marked point processes for three dimensional cellular modeling. These are new areas in which I have recently started investing myself. Over all, I want to become an expert on the computational aspects of Bayesian statistics.