Algunos problemas de estadística computacional

Abstract

This work is focused on providing solutions for some real problems by computational algorithms. In the first place, new Bayesian inference strategies are proposed to improve the parametric estimation for the limit distribution of extreme values. They are aimed at seizing all the information contained in the whole dataset, to ease the lack of data problem, which is frequent in this context. This is implemented by building highly informative priors, taking advantage of the theoretical and/or empirical relations that can be established between the parameters of the baseline distribution and the parameters of the extreme value distribution, which results in more exact and precise estimations. In addition, new spatial models for multivariate extreme distributions associated to climatological events are proposed, by introducing copula models to control spatial dependence. Estimation errors are reduced, in comparison with the models that consider independence. Finally, it is shown how to use symbolic regression to look for the most adequate model for a dataset. This technique allows to find satisfying solutions through genetic evolution of different mathematical expressions, both in shape and parameter values, without the need to previously know their structure. To show its feasibility, it has been applied to surface tension data for alcohols.