Sampling from a multivariate Gaussian distribution truncated on a simplex

a review

Yoann Altmann, Steve McLaughlin, Nicolas Dobigeon

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In many Bayesian models, the posterior distribution of interest is a multivariate Gaussian distribution restricted to a specific domain. In particular, when the unknown parameters to be estimated can be considered as proportions or probabilities, they must satisfy posi-tivity and sum-to-one constraints. This paper reviews recent Monte Carlo methods for sampling from multivariate Gaussian distributions restricted to the standard simplex. First, a classical Gibbs sampler is presented. Then, two Hamiltonian Monte Carlo methods are described and analyzed. In a similar fashion to the Gibbs sampler, the first method has a acceptance rate equal to one whereas the second requires an accept/reject procedure. The performance of the three methods are compared through the use of a few examples.

Original languageEnglish
Title of host publicationIEEE Workshop on Statistical Signal Processing Proceedings
PublisherIEEE
Pages113-116
Number of pages4
ISBN (Print)9781479949755
DOIs
Publication statusPublished - 2014
Event17th IEEE Workshop on Statistical Signal Processing 2014 - Gold Coast, Australia
Duration: 29 Jun 20142 Jul 2014

Conference

Conference17th IEEE Workshop on Statistical Signal Processing 2014
Abbreviated titleSSP 2014
CountryAustralia
CityGold Coast
Period29/06/142/07/14

Fingerprint

Gibbs Sampler
Gaussian distribution
Multivariate Distribution
Monte Carlo method
Monte Carlo methods
Sampling
Hamiltonians
Bayesian Model
Posterior distribution
Unknown Parameters
Proportion
Review
Standards

Keywords

  • Constrained Hamiltonian Monte Carlo
  • Markov Chain Monte Carlo methods
  • truncated multivariate Gaussian distributions

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Applied Mathematics
  • Signal Processing
  • Computer Science Applications

Cite this

Altmann, Y., McLaughlin, S., & Dobigeon, N. (2014). Sampling from a multivariate Gaussian distribution truncated on a simplex: a review. In IEEE Workshop on Statistical Signal Processing Proceedings (pp. 113-116). [6884588] IEEE. https://doi.org/10.1109/SSP.2014.6884588
Altmann, Yoann ; McLaughlin, Steve ; Dobigeon, Nicolas. / Sampling from a multivariate Gaussian distribution truncated on a simplex : a review. IEEE Workshop on Statistical Signal Processing Proceedings. IEEE, 2014. pp. 113-116
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Altmann, Y, McLaughlin, S & Dobigeon, N 2014, Sampling from a multivariate Gaussian distribution truncated on a simplex: a review. in IEEE Workshop on Statistical Signal Processing Proceedings., 6884588, IEEE, pp. 113-116, 17th IEEE Workshop on Statistical Signal Processing 2014, Gold Coast, Australia, 29/06/14. https://doi.org/10.1109/SSP.2014.6884588

Sampling from a multivariate Gaussian distribution truncated on a simplex : a review. / Altmann, Yoann; McLaughlin, Steve; Dobigeon, Nicolas.

IEEE Workshop on Statistical Signal Processing Proceedings. IEEE, 2014. p. 113-116 6884588.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Altmann Y, McLaughlin S, Dobigeon N. Sampling from a multivariate Gaussian distribution truncated on a simplex: a review. In IEEE Workshop on Statistical Signal Processing Proceedings. IEEE. 2014. p. 113-116. 6884588 https://doi.org/10.1109/SSP.2014.6884588