Multivariate Dirichlet moments and a polychromatic Ewens sampling formula
Dello Schiavo L, Quattrocchi F. Multivariate Dirichlet moments and a polychromatic Ewens sampling formula. arXiv, 2309.11292.
Download (ext.)
Preprint
| Draft
| English
Corresponding author has ISTA affiliation
Department
Abstract
We present an elementary non-recursive formula for the multivariate moments
of the Dirichlet distribution on the standard simplex, in terms of the pattern
inventory of the moments' exponents. We obtain analog formulas for the
multivariate moments of the Dirichlet-Ferguson and Gamma measures. We further
introduce a polychromatic analogue of Ewens sampling formula on colored integer
partitions, discuss its relation with suitable extensions of Hoppe's urn model
and of the Chinese restaurant process, and prove that it satisfies an adapted
notion of consistency in the sense of Kingman.
Publishing Year
Date Published
2023-09-20
Journal Title
arXiv
Acknowledgement
This research was funded by the Austrian Science Fund (FWF) ESPRIT 208. For the purpose of open access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission. F.Q. gratefully acknowledges support by the Austrian Science Fund (FWF), Project SFB F65. The authors are grateful to Professor Nathanaël Berestycki for several helpful suggestions, and to Nicola Battisti and Dr. Elizabeth Hollwey for enlightening discussions on DNA-methylation.
Article Number
2309.11292
IST-REx-ID
Cite this
Dello Schiavo L, Quattrocchi F. Multivariate Dirichlet moments and a polychromatic Ewens sampling formula. arXiv. doi:10.48550/arXiv.2309.11292
Dello Schiavo, L., & Quattrocchi, F. (n.d.). Multivariate Dirichlet moments and a polychromatic Ewens sampling formula. arXiv. https://doi.org/10.48550/arXiv.2309.11292
Dello Schiavo, Lorenzo, and Filippo Quattrocchi. “Multivariate Dirichlet Moments and a Polychromatic Ewens Sampling Formula.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2309.11292.
L. Dello Schiavo and F. Quattrocchi, “Multivariate Dirichlet moments and a polychromatic Ewens sampling formula,” arXiv. .
Dello Schiavo L, Quattrocchi F. Multivariate Dirichlet moments and a polychromatic Ewens sampling formula. arXiv, 2309.11292.
Dello Schiavo, Lorenzo, and Filippo Quattrocchi. “Multivariate Dirichlet Moments and a Polychromatic Ewens Sampling Formula.” ArXiv, 2309.11292, doi:10.48550/arXiv.2309.11292.
All files available under the following license(s):
Copyright Statement:
This Item is protected by copyright and/or related rights. [...]
Link(s) to Main File(s)
Access Level
Open Access
Export
Marked PublicationsOpen Data ISTA Research Explorer
Sources
arXiv 2309.11292
Google Scholar