## Electronic Journal of Statistics

### Improving the INLA approach for approximate Bayesian inference for latent Gaussian models

#### Abstract

We introduce a new copula-based correction for generalized linear mixed models (GLMMs) within the integrated nested Laplace approximation (INLA) approach for approximate Bayesian inference for latent Gaussian models. While INLA is usually very accurate, some (rather extreme) cases of GLMMs with e.g. binomial or Poisson data have been seen to be problematic. Inaccuracies can occur when there is a very low degree of smoothing or “borrowing strength” within the model, and we have therefore developed a correction aiming to push the boundaries of the applicability of INLA. Our new correction has been implemented as part of the R-INLA package, and adds only negligible computational cost. Empirical evaluations on both real and simulated data indicate that the method works well.

#### Article information

Source
Electron. J. Statist., Volume 9, Number 2 (2015), 2706-2731.

Dates
First available in Project Euclid: 14 December 2015

https://projecteuclid.org/euclid.ejs/1450103327

Digital Object Identifier
doi:10.1214/15-EJS1092

Mathematical Reviews number (MathSciNet)
MR3433587

Zentralblatt MATH identifier
1329.62127

Subjects
Primary: 62F15: Bayesian inference

#### Citation

Ferkingstad, Egil; Rue, Håvard. Improving the INLA approach for approximate Bayesian inference for latent Gaussian models. Electron. J. Statist. 9 (2015), no. 2, 2706--2731. doi:10.1214/15-EJS1092. https://projecteuclid.org/euclid.ejs/1450103327

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