### 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 language | English |
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Title of host publication | IEEE Workshop on Statistical Signal Processing Proceedings |

Publisher | IEEE |

Pages | 113-116 |

Number of pages | 4 |

ISBN (Print) | 9781479949755 |

DOIs | |

Publication status | Published - 2014 |

Event | 17th IEEE Workshop on Statistical Signal Processing 2014 - Gold Coast, Australia Duration: 29 Jun 2014 → 2 Jul 2014 |

### Conference

Conference | 17th IEEE Workshop on Statistical Signal Processing 2014 |
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Abbreviated title | SSP 2014 |

Country | Australia |

City | Gold Coast |

Period | 29/06/14 → 2/07/14 |

### Fingerprint

### 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

*IEEE Workshop on Statistical Signal Processing Proceedings*(pp. 113-116). [6884588] IEEE. https://doi.org/10.1109/SSP.2014.6884588

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Sampling from a multivariate Gaussian distribution truncated on a simplex

T2 - a review

AU - Altmann, Yoann

AU - McLaughlin, Steve

AU - Dobigeon, Nicolas

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Constrained Hamiltonian Monte Carlo

KW - Markov Chain Monte Carlo methods

KW - truncated multivariate Gaussian distributions

U2 - 10.1109/SSP.2014.6884588

DO - 10.1109/SSP.2014.6884588

M3 - Conference contribution

AN - SCOPUS:84907409502

SN - 9781479949755

SP - 113

EP - 116

BT - IEEE Workshop on Statistical Signal Processing Proceedings

PB - IEEE

ER -