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Open Access research with a European policy impact...

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EPRC is a leading institute in Europe for comparative research on public policy, with a particular focus on regional development policies. Spanning 30 European countries, EPRC research programmes have a strong emphasis on applied research and knowledge exchange, including the provision of policy advice to EU institutions and national and sub-national government authorities throughout Europe.

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Probability density decomposition for conditionally dependent random variables modeled by Vines

Bedford, T.J. and Cooke, R. (2001) Probability density decomposition for conditionally dependent random variables modeled by Vines. Annals of Mathematics and Artificial Intelligence, 32 (1). pp. 245-268. ISSN 1012-2443

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Abstract

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 lsquocanonical vinesrsquo built on highest degree trees offer the most efficient structure for Gibbs sampling.