Extreme value for paleoclimatic data sets with an application in lichenometry

To study marked peaks, abrupt changes and outliers in paleoclimatic data sets, it is important to develop statistical methodologies that are specially tailored to these extremes. This is especially fundamental because the definition of extreme events depends on the magnitude of any intrinsic thresholds and, consequently, the linearity of classical statistical tools based on averages is not anymore adapted. Although the statistics of extremes have played a central role in engineering practice for water resources management (floods) as well as in finance, extreme value theory has rarely been applied to the analysis of paleoclimatic data sets. The central theme of this talk is an application of the probabilistic theory of extreme values to the study of the largest lichen diameters from different moraines around the world. The advantage of this strategy over classical statistical lichenometric analyzes is that the uncertainties associated with studying the largest lichen diameters is fully taken into account through identification of the distribution of these largest diameters. In addition to providing a probabilistic framework, the flexibility of our statistical model allows to deal with situations where the chronological order of the moraines is either known or unknown. To validate our statistical methodology, simulated examples were analyzed and tested. Finally, the proposed techniques were applied to different sites from Bolivia and other regions.