Abstract

We study the relationship between partial correlation and constant conditional correlation with particular attention to copulae used in high dimensional graphical models. Sufficient and, in some cases, necessary conditions for equality are obtained. Numerical results show that the difference between partial and conditional correlation is small for the minimum information copula. When approximate equality holds, regular vines enable us to specify a correlation structure without algebraic constrains (e.g. positive definiteness) and to translate this structure into an on-the-fly sampling algorithm.Keywords and phrasesPartial correlationconditional correlationconditional independenceMarkov treecopulaentropyinformationreliability model

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