### Abstract

Language | English |
---|---|

Pages | 1031-1068 |

Number of pages | 37 |

Journal | Annals of Statistics |

Volume | 30 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2002 |

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### Keywords

- correlation
- monte carlo simulation
- statistics
- management theory

### Cite this

*Annals of Statistics*,

*30*(4), 1031-1068. https://doi.org/10.1214/aos/1031689016

}

*Annals of Statistics*, vol. 30, no. 4, pp. 1031-1068. https://doi.org/10.1214/aos/1031689016

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Vines - A new graphical model for dependent random variables

AU - Bedford, T.J.

AU - Cooke, R.

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

KW - correlation

KW - monte carlo simulation

KW - statistics

KW - management theory

UR - http://dx.doi.org/10.1214/aos/1031689016

U2 - 10.1214/aos/1031689016

DO - 10.1214/aos/1031689016

M3 - Article

VL - 30

SP - 1031

EP - 1068

JO - Annals of Statistics

T2 - Annals of Statistics

JF - Annals of Statistics

SN - 0090-5364

IS - 4

ER -