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Bayesian computing with INLA: a review

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

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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 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.
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Original languageEnglish
Pages (from-to)395-421
Number of pages17
JournalAnnual Review of Statistics and its Application
Volume4
DOIs
StatePublished - Apr 2017

    Research areas

  • Gaussian Markov random field, Laplace approximations, Approximate Bayesian inference, Latest Gaussian models, Numerical integration, Sparse matrices

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