Conditional independence among max-stable laws

Logical Properties of Stable Conditional Independence

We utilize recent results concerning a complete axiomatization of stable conditional independence (CI) relative to discrete probability measures to derive perfect model properties of stable CI structures. We show that stable CI can be interpreted as a generalization of undirected graphical models and establish a connection between sets of stable CI statements and propositional formulae in conju...

Propositional Independence Conditional independence

Independence – the study of what is relevant to a given problem of reasoning – is an important AI topic. In this paper, we investigate several notions of conditional independence in propositional logic: Darwiche and Pearl’s conditional independence, and two more restricted forms of it, called strong conditional independence and perfect conditional independence. Many characterizations and proper...

Prediction for Max-Stable Processes via an Approximated Conditional Density

The dependence structure of a max-stable random vector is characterized by its spectral measure. Using only the spectral measure, we present a method for approximating the conditional density of an unobserved component of a max-stable random vector given the other components of the vector. The approximated conditional density can be used for prediction. Additionally, we present a new parametric...

Logical and algorithmic properties of stable conditional independence

The logical and algorithmic properties of stable conditional independence (CI) as an alternative structural representation of conditional independence information are investigated. We utilize recent results concerning a complete axiomatization of stable conditional independence relative to discrete probability measures to derive perfect model properties of stable conditional independence struct...

Conditional Independence