Vines - A new graphical model for dependent random variables

T.J. Bedford, R. Cooke

Research output: Contribution to journalArticle

511 Citations (Scopus)

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.
LanguageEnglish
Pages1031-1068
Number of pages37
JournalAnnals of Statistics
Volume30
Issue number4
DOIs
Publication statusPublished - 2002

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Dependent Random Variables
Graphical Models
Spearman's coefficient
Partial Correlation
Generalise
Uncertainty Analysis
Conditional Independence
Multivariate Normal Distribution
Multivariate Distribution
Marginal Distribution
Unknown Parameters
High-dimensional
Graphical models
Random variables
Restriction
Uncertainty
Output
Modeling

Keywords

  • correlation
  • monte carlo simulation
  • statistics
  • management theory

Cite this

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Vines - A new graphical model for dependent random variables. / Bedford, T.J.; Cooke, R.

In: Annals of Statistics, Vol. 30, No. 4, 2002, p. 1031-1068.

Research output: Contribution to journalArticle

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AU - Bedford, T.J.

AU - Cooke, R.

PY - 2002

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