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Bayesian computing with INLA: a review

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

In: Annual Review of Statistics and its Application, Vol. 4, 03.2017, p. 395-421.

Research output: Contribution to journalReview articlepeer-review

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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

APA

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

Vancouver

Rue H, Riebler A, Sørbye SH, Illian JB, Simpson DP, Lindgren FK. Bayesian computing with INLA: a review. Annual Review of Statistics and its Application. 2017 Mar;4:395-421. https://doi.org/10.1146/annurev-statistics-060116-054045

Author

Rue, Håvard ; 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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@article{9e978694021d47fda082e0e7970a70b3,
title = "Bayesian computing with INLA: a review",
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 will 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.",
keywords = "Gaussian Markov random field, Laplace approximations, Approximate Bayesian inference, Latest Gaussian models, Numerical integration, Sparse matrices",
author = "H{\aa}vard Rue and Andrea Riebler and S{\o}rbye, {Sigrunn H.} and Illian, {Janine B.} and Simpson, {Daniel P.} and Lindgren, {Finn K.}",
year = "2017",
month = mar,
doi = "10.1146/annurev-statistics-060116-054045",
language = "English",
volume = "4",
pages = "395--421",
journal = "Annual Review of Statistics and its Application",
issn = "2326-8298",
publisher = "Annual Reviews Inc.",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Bayesian computing with INLA

T2 - a review

AU - Rue, Håvard

AU - Riebler, Andrea

AU - Sørbye, Sigrunn H.

AU - Illian, Janine B.

AU - Simpson, Daniel P.

AU - Lindgren, Finn K.

PY - 2017/3

Y1 - 2017/3

N2 - 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 will 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.

AB - 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 will 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.

KW - Gaussian Markov random field

KW - Laplace approximations

KW - Approximate Bayesian inference

KW - Latest Gaussian models

KW - Numerical integration

KW - Sparse matrices

U2 - 10.1146/annurev-statistics-060116-054045

DO - 10.1146/annurev-statistics-060116-054045

M3 - Review article

VL - 4

SP - 395

EP - 421

JO - Annual Review of Statistics and its Application

JF - Annual Review of Statistics and its Application

SN - 2326-8298

ER -

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