Sampling, conditionalizing, counting, merging, searching regular vines
Cooke, R.M. and Kurowicka, D. and Wilson, K. (2015) Sampling, conditionalizing, counting, merging, searching regular vines. Journal of Multivariate Analysis. ISSN 0047-259X (https://doi.org/10.1016/j.jmva.2015.02.001)
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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 $2^{n-1}$ 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.
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Item type: Article ID code: 51764 Dates: DateEvent2015Published14 February 2015Published Online2 February 2015AcceptedSubjects: Science > Mathematics > Probabilities. Mathematical statistics Department: Strathclyde Business School > Management Science Depositing user: Pure Administrator Date deposited: 18 Feb 2015 16:37 Last modified: 03 Nov 2024 01:52 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/51764