Integrating Entropy and Copula Theories for Hydrologic Modeling and Analysis

Entropy is a measure of uncertainty and has been commonly used for various applications, including probability inferences in hydrology. Copula has been widely used for constructing joint distributions to model the dependence structure of multivariate hydrological random variables. Integration of entropy and copula theories provides new insights in hydrologic modeling and analysis, for which the development and application are still in infancy. Two broad branches of integration of the two concepts, entropy copula and copula entropy, are introduced in this study. On the one hand, the entropy theory can be used to derive new families of copulas based on information content matching. On the other hand, the copula entropy provides attractive alternatives in the nonlinear dependence measurement even in higher dimensions. We introduce in this study the integration of entropy and copula theories in the dependence modeling and analysis to illustrate the potential applications in hydrology and water resources

State Estimation for Distributed Systems with Stochastic and Set-membership Uncertainties

State estimation techniques for centralized, distributed, and decentralized systems are studied. An easy-to-implement state estimation concept is introduced that generalizes and combines basic principles of Kalman filter theory and ellipsoidal calculus. By means of this method, stochastic and set-membership uncertainties can be taken into consideration simultaneously. Different solutions for implementing these estimation algorithms in distributed networked systems are presented

Link between Copula and Tomography

An important problem in statistics is to determine a joint probability distribution from its marginals and an important problem in Computed Tomography (CT) is to reconstruct an image from its projections. In the bivariate case, the marginal probability density functions f1(x) and f2(y) are related to their joint distribution f(x, y) via horizontal and vertical line integrals. Interestingly, this is also the case of a very limited angle X ray CT problem where f(x, y) is an image representing the distribution of the material density and f1(x), f2(y) are the horizontal and vertical line integrals. The problem of determining f(x, y) from f1(x) and f2(y) is an ill-posed undetermined inverse problem. In statistics the notion of copula is exactly introduced to characterize all the possible solutions to the problem of reconstructing a bivariate density from its marginals. In this paper, we elaborate on the possible link between Copula and CT and try to see whether we can use the methods used in one domain into the other