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Communication Dans Un Congrès Année : 2014

Sampling from a multivariate gaussian distribution truncated on a simplex: a review

Résumé

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 positivity 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.
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Dates et versions

hal-04080915 , version 1 (25-04-2023)

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Yoann Altmann, Steve Mclaughlin, Nicolas Dobigeon. Sampling from a multivariate gaussian distribution truncated on a simplex: a review. IEEE Workshop on Statistical Signal Processing (SSP 2014), IEEE, Jun 2014, Gold Coast, Australia. pp.113-116, ⟨10.1109/SSP.2014.6884588⟩. ⟨hal-04080915⟩
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