### Abstract

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

Number of pages | 25 |

Journal | Journal of Multivariate Analysis |

Early online date | 14 Feb 2015 |

DOIs | |

Publication status | Published - 2015 |

### Fingerprint

### Keywords

- regular vines
- number of regular vines
- vine conditionalization
- vine merging

### Cite this

*Journal of Multivariate Analysis*. https://doi.org/10.1016/j.jmva.2015.02.001

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*Journal of Multivariate Analysis*. https://doi.org/10.1016/j.jmva.2015.02.001

**Sampling, conditionalizing, counting, merging, searching regular vines.** / Cooke, R.M.; Kurowicka, D.; Wilson, K.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Sampling, conditionalizing, counting, merging, searching regular vines

AU - Cooke, R.M.

AU - Kurowicka, D.

AU - Wilson, K.

PY - 2015

Y1 - 2015

N2 - We present a sampling algorithm for a regular vine on $n$ variables which starts at an arbitrary variable. A sampling order whose nested conditional probabilities can be written as products of (conditional) copulas in the vine and univariate margins is said to be implied by the regular vine. We show that there are $2^{n-1}$ implied sampling orders for any regular vine on $n$ variables. We show that two regular vines on $n$ and $m$ distinct variables can be merged in $2^{n+m-2}$ ways. This greatly simplifies the proof of the number of regular vines on $n$ variables. A notion of sampling proximity based on numbers of shared implied sampling orders is introduced, and we use this notion to define a heuristic for searching vine space that avoids proximate vines.

AB - We present a sampling algorithm for a regular vine on $n$ variables which starts at an arbitrary variable. A sampling order whose nested conditional probabilities can be written as products of (conditional) copulas in the vine and univariate margins is said to be implied by the regular vine. We show that there are $2^{n-1}$ implied sampling orders for any regular vine on $n$ variables. We show that two regular vines on $n$ and $m$ distinct variables can be merged in $2^{n+m-2}$ ways. This greatly simplifies the proof of the number of regular vines on $n$ variables. A notion of sampling proximity based on numbers of shared implied sampling orders is introduced, and we use this notion to define a heuristic for searching vine space that avoids proximate vines.

KW - regular vines

KW - number of regular vines

KW - vine conditionalization

KW - vine merging

UR - http://www.sciencedirect.com/science/article/pii/S0047259X15000366

U2 - 10.1016/j.jmva.2015.02.001

DO - 10.1016/j.jmva.2015.02.001

M3 - Article

JO - Journal of Multivariate Analysis

T2 - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

ER -