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Sampling, conditionalizing, counting, merging, searching regular vines

Lookup NU author(s): Professor Kevin Wilson

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Abstract

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 2ⁿ⁻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.

Publication metadata

Author(s): Cooke RM, Kurowicka D, Wilson K

Publication type: Article

Publication status: Published

Journal: Journal of Multivariate Analysis

Year: 2015

Volume: 138

Pages: 4-18

Print publication date: 01/06/2015

Online publication date: 14/02/2015

Acceptance date: 03/02/2015

Date deposited: 08/09/2015

ISSN (print): 0047-259X

ISSN (electronic): 1095-7243

Publisher: Elsevier Inc.

URL: http://dx.doi.org/10.1016/j.jmva.2015.02.001

DOI: 10.1016/j.jmva.2015.02.001

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