A new graphical model, called a vine, for dependent random variables is introduced. Vines generalize the Markov trees often used in modelling high-dimensional distributions. They differ from Markov trees and Bayesian belief nets in that the concept of conditional independence is weakened to allow for various forms of conditional dependence.

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Vines: A new graphical model for dependent random variables

A vine is a new graphical model for dependent random variables Vines generalize the Markov trees often used in modeling multivariate distributions They differ from Markov trees and Bayesian belief nets in that the concept of conditional independence is weakened to allow for various forms of conditional dependence A general formula for the density of a vine dependent distribution is derived This generalizes the well-known density formula for belief nets based on the decomposition of belief nets into cliques Furthermore, the formula allows a simple proof of the Information Decomposition Theorem for a regular vine The problem of (conditional) sampling is discussed, and Gibbs sampling is proposed to carry out sampling from conditional vine dependent distributions The so-called ‘canonical vines’ built on highest degree trees offer the most efficient structure for Gibbs sampling

Probability Density Decomposition for Conditionally Dependent Random Variables Modeled by Vines

Eliciting conditional and unconditional rank correlations from conditional probabilities

Expert judgement for dependence in probabilistic modelling: a systematic literature review and future research directions

The entropy theory has been widely applied in hydrology for probability inference based on incomplete information and the principle of maximum entropy. Meanwhile, copulas have been extensively used for multivariate analysis and modeling the dependence structure between hydrologic and climatic variables. The underlying assumption of the principle of maximum entropy is that the entropy variables are mutually independent from each other. The principle of maximum entropy can be combined with the copula concept for describing the probability distribution function of multiple dependent variables and their dependence structure. Recently, efforts have been made to integrate the entropy and copula concepts (hereafter, entropy–copula) in various forms to take advantage of the strengths of both methods. Combining the two concepts provides new insight into the probability inference; however, limited studies have utilized the entropy–copula methods in hydrology and climatology. In this paper, the currently ava...

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Entropy–Copula in Hydrology and Climatology

Minimum information bivariate distributions with uniform marginals and a specified rank correlation are studied in this paper. These distributions play an important role in a particular way of modeling dependent random variables which has been used in the computer code UNICORN for carrying out uncertainty analyses. It is shown that these minimum information distributions have a particular form which makes simulation of conditional distributions very simple. Approximations to the continuous distributions are discussed and explicit formulae are determined. Finally a relation is discussed to DAD theorems, and a numerical algorithm is given (which has geometric rate of covergence) for determining the minimum information distributions.

A.M.H. Meeuwissen

Papers

Minimally informative distributions with given rank correlation for use in uncertainty analysis