Stochastic Modeling of Hydroclimatic Processes Using Vine Copulas

The generation of synthetic time series is important in contemporary water sciences for their wide applicability and ability to model environmental uncertainty. Hydroclimatic variables often exhibit highly skewed distributions, intermittency (that is, alternating dry and wet intervals), and spatial and temporal dependencies that pose a particular challenge to their study. Vine copula models offer an appealing approach to generate synthetic time series because of their ability to preserve any marginal distribution while modeling a variety of probabilistic dependence structures. In this work, we focus on the stochastic modeling of hydroclimatic processes using vine copula models. We provide an approach to model intermittency by coupling Markov chains with vine copula models. Our approach preserves first-order auto- and cross-dependencies (correlation). Moreover, we present a novel framework that is able to model multiple processes simultaneously. This method is based on the coupling of temporal and spatial dependence models through repetitive sampling. The result is a parsimonious and flexible method that can adequately account for temporal and spatial dependencies. Our method is illustrated within the context of a recent reliability assessment of a historical hydraulic structure in central Mexico. Our results show that by ignoring important characteristics of probabilistic dependence that are well captured by our approach, the reliability of the structure could be severely underestimated.

A statistical theory of the strength of epidemics: an application to the Italian COVID-19 case

The proposed theory defines a relative index of epidemic lethality that compares any two configurations in different observation periods, preferably one in the acute and the other in a mild epidemic phase. Raw mortality data represent the input, with no need to recognize the cause of death. Data are categorized according to the victims’ age, which must be renormalized because older people have a greater probability of developing a level of physical decay (human damage), favouring critical pathologies and co-morbidities. The probabilistic dependence of human damage on renormalized age is related to a death criterion considering a virus spread by contagion and our capacity to cure the disease. Remarkably, this is reminiscent of the Weibull theory of the strength of brittle structures containing a population of crack-like defects, in the correlation between the statistical distribution of cracks and the risk of fracture at a prescribed stress level. Age-of-death scaling laws are predicted in accordance with data collected in Italian regions and provinces during the first wave of COVID-19, taken as representative examples to validate the theory. For the prevention of spread and the management of the epidemic, the various parameters of the theory shall be informed on other existing epidemiological models.

MODELLING DEPENDENCE IN DEMPSTER-SHAFER THEORY

Belief functions can only be combined by Dempster's rule when they are based on independent items of evidence. This paper proposes a method for handling the case where there is some probabilistic dependence among the items of evidence. The method relies on compact representations of joint probability distributions on the assumption variables associated with the belief functions. These distributions are then used to compute degrees of support of hypotheses of interest. It is shown that the theory of hints is the appropriate general framework for this method.