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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 

References

Allenby, G. M. and Rossi, P. (1999). Marketing models of consumer heterogeneity. J. Econometrics 89, 57–78.Google Scholar
Devroye, L. (1986). Non-Uniform Random Variate Generation. Springer, New York.Google Scholar
Gelfand, A. E. and Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85, 398–409.CrossRefGoogle Scholar
Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Machine Intelligence 6, 721–741.Google Scholar
Geweke, J. (1991). Efficient simulation from the Multivariate Normal and Student t-distribution subject to linear constrains. In Computing Sciences and Statistics (Proc. 23rd Symp. Interface), American Statistical Association, pp. 571–577.Google Scholar
Geweke, J., Keane, M. and Runkle, D. (1997). Statistical inference in the multinomial multiperiod probit model. J. Econometrics 80, 125–165.Google Scholar
Møller, J. (1999). Perfect simulation of conditionally specified models. J. R. Statist. Soc. B 61, 251–264.Google Scholar
Murdoch, D. J. and Green, P. J. (1998). Exact sampling from a continuous state space. Scand. J. Statist. 25, 483–502.CrossRefGoogle Scholar
Philippe, A. and Robert, C. (2003). Perfect simulation of positive Gaussian distributions. Statist. Comput. 13, 179–186.Google Scholar
Propp, J. G. and Wilson, D. B. (1996). Exact sampling with coupled Markov chains and applications to statistical mechanics. Random Structures Algorithms 9, 223–252.Google Scholar
Robert, C. (1995). Simulation of truncated normal random variables. Statist. Comput. 5, 121–125.Google Scholar
Rubin, D. B. (1987). Multiple Imputations for Nonresponse in Surveys. John Wiley, New York.Google Scholar
Tanner, M. A. (1991). Tools for Statistical Inference. Observed Data and Data Augmentation Methods (Lecture Notes Statist. 67). Springer, New York.Google Scholar
Tanner, M. A. and Wong, W. (1987). The calculation of posterior distributions by data augmentation. J. Amer. Statist. Assoc. 82, 528–549.Google Scholar
Thorisson, H. (2000). Coupling, Stationarity, and Regeneration. Springer, New York.Google Scholar
Wilson, D. B. (1998). Annotated bibliography of perfectly random sampling with Markov chains. In Microsurveys in Discrete Probability (DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 41), eds Aldous, D. and Propp, J., American Mathematical Society, Providence, RI, pp. 209–220. Updated version available at http://dimacs.rutgers.edu/∼dbwilson/exact.Google Scholar