Statistics and Computing

, Volume 23, Issue 4, pp 501–521

Iterative numerical methods for sampling from high dimensional Gaussian distributions

Article

DOI: 10.1007/s11222-012-9326-8

Cite this article as:
Aune, E., Eidsvik, J. & Pokern, Y. Stat Comput (2013) 23: 501. doi:10.1007/s11222-012-9326-8

Abstract

Many applications require efficient sampling from Gaussian distributions. The method of choice depends on the dimension of the problem as well as the structure of the covariance- (Σ) or precision matrix (Q). The most common black-box routine for computing a sample is based on Cholesky factorization. In high dimensions, computing the Cholesky factor of Σ or Q may be prohibitive due to accumulation of more non-zero entries in the factor than is possible to store in memory. We compare different methods for computing the samples iteratively adapting ideas from numerical linear algebra. These methods assume that matrix vector products, Qv, are fast to compute. We show that some of the methods are competitive and faster than Cholesky sampling and that a parallel version of one method on a Graphical Processing Unit (GPU) using CUDA can introduce a speed-up of up to 30x. Moreover, one method is used to sample from the posterior distribution of petroleum reservoir parameters in a North Sea field, given seismic reflection data on a large 3D grid.

Keywords

Gaussian distribution Krylov methods Numerical linear algebra Sampling 

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Norwegian University of Science and TechnologyTrondheimNorway
  2. 2.University College, LondonLondonUK