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An accept-reject algorithm for the positive multivariate normal distribution

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  • Carsten Botts

Abstract

The need to simulate from a positive multivariate normal distribution arises in several settings, specifically in Bayesian analysis. A variety of algorithms can be used to sample from this distribution, but most of these algorithms involve Gibbs sampling. Since the sample is generated from a Markov chain, the user has to account for the fact that sequential draws in the sample depend on one another and that the sample generated only follows a positive multivariate normal distribution asymptotically. The user would not have to account for such issues if the sample generated was i.i.d. In this paper, an accept-reject algorithm is introduced in which variates from a positive multivariate normal distribution are proposed from a multivariate skew-normal distribution. This new algorithm generates an i.i.d. sample and is shown, under certain conditions, to be very efficient. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Carsten Botts, 2013. "An accept-reject algorithm for the positive multivariate normal distribution," Computational Statistics, Springer, vol. 28(4), pages 1749-1773, August.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:4:p:1749-1773
    DOI: 10.1007/s00180-012-0377-2
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    References listed on IDEAS

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    Cited by:

    1. Z. I. Botev, 2017. "The normal law under linear restrictions: simulation and estimation via minimax tilting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 125-148, January.

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