The Annals of Statistics

Vines--a new graphical model for dependent random variables

Tim Bedford and Roger M. Cooke

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Abstract

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.

Vines can be used to specify multivariate distributions in a straightforward way by specifying various marginal distributions and the ways in which these marginals are to be coupled. Such distributions have applications in uncertainty analysis where the objective is to determine the sensitivity of a model output with respect to the uncertainty in unknown parameters. Expert information is frequently elicited to determine some quantitative characteristics of the distribution such as (rank) correlations. We show that it is simple to construct a minimum information vine distribution, given such expert information. Sampling from minimum information distributions with given marginals and (conditional) rank correlations specified on a vine can be performed almost as fast as independent sampling. A special case of the vine construction generalizes work of Joe and allows the construction of a multivariate normal distribution by specifying a set of partial correlations on which there are no restrictions except the obvious one that a correlation lies between $-1$ and 1.

Article information

Source
Ann. Statist., Volume 30, Number 4 (2002), 1031-1068.

Dates
First available in Project Euclid: 10 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1031689016

Digital Object Identifier
doi:10.1214/aos/1031689016

Mathematical Reviews number (MathSciNet)
MR1926167

Zentralblatt MATH identifier
1101.62339

Subjects
Primary: 62E10: Characterization and structure theory 62E25 62H20: Measures of association (correlation, canonical correlation, etc.) 62B10: Information-theoretic topics [See also 94A17] 94A17: Measures of information, entropy

Keywords
Correlation dependence information multivariate probablility distribution Monte Carlo simulation tree dependence Markov tree belief net multivariate normal distribution

Citation

Bedford, Tim; Cooke, Roger M. Vines--a new graphical model for dependent random variables. Ann. Statist. 30 (2002), no. 4, 1031--1068. doi:10.1214/aos/1031689016. https://projecteuclid.org/euclid.aos/1031689016


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