389
Views
29
CrossRef citations to date
0
Altmetric
Original Articles

Efficient Sampling Methods for Truncated Multivariate Normal and Student-t Distributions Subject to Linear Inequality Constraints

&
Pages 712-732 | Received 12 Oct 2014, Accepted 05 Dec 2014, Published online: 23 Apr 2015

References

  • Breslaw, J. 1994. Random sampling from a truncated multivariate normal distribution. Appl. Math. Lett., 7(1), 1–6.
  • Damien, P., and S. G. Walker. 2001. Sampling truncated normal, beta, and gamma densities. J. Comput. Graph. Stat., 10(2), 206–215.
  • Gelfand, A. E., and A. F. M. Smith. 1990. Sampling-based approaches to calculating marginal densities. J. Am. Stat. Assoc., 85(410), 398–409.
  • Gelfand, A. E., A. F. M. Smith, and T.–M. Lee. 1992. Bayesian analysis of constrained parameter and truncated data problems using Gibbs sampling. J. Am. Stat. Assoc., 87(418), 523–532.
  • Geman, S., and D. Geman. 1984. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Machine Intell., PAMI-6, 721–741.
  • Geweke, J. 1991. Efficient simulation from the multivariate normal and Student-t distributions subject to linear constraints and the evaluation of constraint probabilities. In Computing science and statistics: Proceedings of the 23rd Symposium on the Interface, ed. E. M. Keramidas, 571–578. Fairfax Station, VA: Interface Foundation of North America, Inc.
  • Geweke, J. 1996. Bayesian inference for linear models subject to linear inequality constraints. In Modelling and prediction: Honoring Seymour Geisser, ed. J. C. Lee, W. O. Johnson, and A. Zellner, 248–263. New York, NY: Springer.
  • Gómez-Sánchez-Manzano, E., M. Gómez-Villegas, and J. Marín. 2008. Multivariate exponential power distributions as mixtures of normal distributions with bayesian applications. Commun. Stat. Theory Methods, 37(6), 972–985.
  • Hajivassiliou, V. A., and D. L. Mcfadden, 1990. The method of simulated scores for the estimation of ldv models: With an application to the problem of external debt crises. Cowles Foundation Discussion Paper no. 967. https://ideas.repec.org/p/cwl/cwldpp/967.html
  • Horrace, W. C. 2005. Some results on the multivariate truncated normal distribution. J. Multivariate Anal., 94(1), 209–221.
  • Liechty, M. W., and J. Lu. 2010. Multivariate normal slice sampling. J. Comput. Graph. Stat., 19(2), 281–294. With supplementary material available online.
  • Neal, R. M. 2003. Slice sampling. Ann. Stat., 31(3), 705–767. With discussions and a rejoinder by the author.
  • Robert, C. P. 1995. Simulation of truncated normal variables. Stat. Comput., 5, 121–125.
  • Robert, C. P., and G. Casella. 2004. Monte Carlo statistical methods. 2nd ed. Springer Texts in Statistics. New York, NY: Springer-Verlag.
  • Rodrigues-Yam, G., R. A. Davis, and L. L. Scharf. 2004. Efficient Gibbs sampling of truncated multivariate normal with application to constrained linear regression. Technical report, Colorado State University, Fort Collins, CO.
  • Tierney, L. 1994. Markov chains for exploring posterior distributions. Ann. Stat., 22(4), 1701–1762. With discussion and a rejoinder by the author.
  • Yu, J., and G. Tian. 2011. Efficient algorithms for generating truncated multivariate normal distributions. Acta Math. Appl. Sin. (English Ser.), 27, 601–612.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.