Two statistical methods for improving the analysis of large climatic data sets:: General skewed Kalman filters and distributions of distributions

This research focuses on two original statistical methods for analyzing large data sets in the context of climate studies. First, we propose a new way to introduce skewness to state-space models without losing the computational advantages of the Kalman filter operations. The motivation stems from the popularity of state-space models and statistical data assimilation techniques in geophysics, specially for forecasting purposes in real time. The added skewness comes from the extension of the multivariate normal distribution to the general multivariate skew-normal distribution. A new specific state-space model for which the Kalman Filtering operations are carefully described is derived. The second part of this work is dedicated to the extension of clustering methods into the distributions of distributions framework. This concept allows us to cluster distributions, instead of simple observations. To illustrate the applicability of such a method, we analyze the distributions of 16200 temperature and humidity vertical profiles. Different levels of dependencies between these distributions are modeled by copulas. The distributions of distributions are decomposed as mixtures and the algorithm to estimate the parameters of such mixtures is presented. Besides providing realistic climatic classes, this clustering method allows atmospheric scientists to explore large climate data sets into a more meaningful and global framework.