Bayesian computing with INLA: a review

Rue, H., Riebler, A., Sørbye, S. H., Illian, J. B. , Simpson, D. P. and Lindgren, F. K. (2017) Bayesian computing with INLA: a review. Annual Review of Statistics and Its Application, 4(1), pp. 395-421. (doi:10.1146/annurev-statistics-060116-054045)

Rue, H., Riebler, A., Sørbye, S. H., Illian, J. B. , Simpson, D. P. and Lindgren, F. K. (2017) Bayesian computing with INLA: a review. Annual Review of Statistics and Its Application, 4(1), pp. 395-421. (doi:10.1146/annurev-statistics-060116-054045)

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Abstract

The key operation in Bayesian inference is to compute high-dimensional integrals. An old approximate technique is the Laplace method or approximation, which dates back to Pierre-Simon Laplace (1774). This simple idea approximates the integrand with a second-order Taylor expansion around the mode and computes the integral analytically. By developing a nested version of this classical idea, combined with modern numerical techniques for sparse matrices, we obtain the approach of integrated nested Laplace approximations (INLA) to do approximate Bayesian inference for latent Gaussian models (LGMs). LGMs represent an important model abstraction for Bayesian inference and include a large proportion of the statistical models used today. In this review, we discuss the reasons for the success of the INLA approach, the R-INLA package, why it is so accurate, why the approximations are very quick to compute, and why LGMs make such a useful concept for Bayesian computing.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Illian, Professor Janine
Authors: Rue, H., Riebler, A., Sørbye, S. H., Illian, J. B., Simpson, D. P., and Lindgren, F. K.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Annual Review of Statistics and Its Application
Publisher:Annual Reviews
ISSN:2326-8298
ISSN (Online):2326-831X
Published Online:23 December 2016

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