Bayesian computing with INLA

a review

Havard Rue, Andrea Riebler, Sigrunn H. Sørbye, Janine B. Illian, Daniel P. Simpson, Finn K. Lindgren

Research output: Contribution to journalReview article

56 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)395-421
Number of pages27
JournalAnnual Review of Statistics and Its Application
Volume4
Early online date23 Dec 2016
DOIs
Publication statusPublished - 7 Mar 2017

Fingerprint

Laplace Approximation
Gaussian Model
Computing
Bayesian inference
Approximate Bayesian Inference
Laplace's Method
Taylor Expansion
Sparse matrix
Integrand
Numerical Techniques
Laplace
Date
Statistical Model
Proportion
High-dimensional
Review
Integrated nested Laplace approximation
Approximation
Integral

Keywords

  • Approximate Bayesian inference
  • Gaussian Markov random fields
  • Laplace approximations
  • Latent Gaussian models
  • Numerical integration
  • Sparse matrices

Cite this

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

Bayesian computing with INLA : a review. / Rue, Havard; Riebler, Andrea; Sørbye, Sigrunn H.; Illian, Janine B.; Simpson, Daniel P.; Lindgren, Finn K.

In: Annual Review of Statistics and Its Application, Vol. 4, 07.03.2017, p. 395-421.

Research output: Contribution to journalReview article

Rue, H, Riebler, A, Sørbye, SH, Illian, JB, Simpson, DP & Lindgren, FK 2017, 'Bayesian computing with INLA: a review', Annual Review of Statistics and Its Application, vol. 4, pp. 395-421. https://doi.org/10.1146/annurev-statistics-060116-054045
Rue, Havard ; Riebler, Andrea ; Sørbye, Sigrunn H. ; Illian, Janine B. ; Simpson, Daniel P. ; Lindgren, Finn K. / Bayesian computing with INLA : a review. In: Annual Review of Statistics and Its Application. 2017 ; Vol. 4. pp. 395-421.
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