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Perfectly random sampling of truncated multinormal distributions

Part of: Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  01 July 2016

Pedro J. Fernández ,
Pablo A. Ferrari  and
Sebastian P. Grynberg
Pedro J. Fernández*
Affiliation:
Fundação Getulio Vargas
Pablo A. Ferrari*
Affiliation:
Universidade de São Paulo
Sebastian P. Grynberg*
Affiliation:
Universidad de Buenos Aires
*
∗ Postal address: Fundação Getulio Vargas, Av. Canal Marapendi 2915, Bloco. 1, Apto. 1502, Barra da Tijuca, Rio de Janeiro, 22631-050, Brazil.
∗∗ Postal address: Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, São Paulo, 05311-970, Brazil. Email address: pablo@ime.usp.br
∗∗∗ Postal address: Departamento de Matemática, Facultad de Ingeniería, Universidad de Buenos Aires, Paseo Colón 850, Buenos Aires, 1063, Argentina.
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Abstract

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The target measure μ is the distribution of a random vector in a box ℬ, a Cartesian product of bounded intervals. The Gibbs sampler is a Markov chain with invariant measure μ. A ‘coupling from the past’ construction of the Gibbs sampler is used to show ergodicity of the dynamics and to perfectly simulate μ. An algorithm to sample vectors with multinormal distribution truncated to ℬ is then implemented.

Keywords

Perfect samplingsimulationnormal distribution

MSC classification

Primary: 65C35: Stochastic particle methods
Secondary: 65C05: Monte Carlo methods
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 39 , Issue 4 , December 2007 , pp. 973 - 990
Copyright
Copyright © Applied Probability Trust 2007 

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