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

18 Citations (Scopus)


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
Number of pages4
ISBN (Print)9781479949755
Publication statusPublished - 2014
Event17th IEEE Workshop on Statistical Signal Processing 2014 - Gold Coast, Australia
Duration: 29 Jun 20142 Jul 2014


Conference17th IEEE Workshop on Statistical Signal Processing 2014
Abbreviated titleSSP 2014
CityGold Coast


  • 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


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