Campus Units

Statistics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

2007

Journal or Book Title

Journal of Computational and Graphical Statistics

Volume

16

Issue

3

First Page

692

Last Page

708

DOI

10.1198/106186007X238431

Abstract

Methods for simulation from multivariate Gaussian distributions restricted to be from outside an arbitrary ellipsoidal region are often needed in applications. A standard rejection algorithm that draws a sample from a multivariate Gaussian distribution and accepts it if it is outside the ellipsoid is often employed: however, this is computationally inefficient if the probability of that ellipsoid under the multivariate normal distribution is substantial. We provide a two-stage rejection sampling scheme for drawing samples from such a truncated distribution. Experiments show that the added complexity of the two-stage approach results in the standard algorithm being more efficient for small ellipsoids (i.e. with small rejection probability). However, as the size of the ellipsoid increases, the efficiency of the two-stage approach relative to the standard algorithm increases indefinitely. The relative efficiency also increases as the number of dimensions increases, as the centers of the ellipsoid and the multivariate Gaussian distribution come closer, and as the shape of the ellipsoid becomes more spherical. We provide results of simulation experiments conducted to quantify the relative efficiency over a range of parameter settings.

Comments

This is an accepted manuscript of an article published by Taylor & Francis in Journal of Computational and Graphical Statistics in 2007, available online: http://dx.doi.org/10.1198/106186007X238431.

Copyright Owner

American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America

Language

en

File Format

application/pdf

Published Version

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