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

arXiv: https://arxiv.org/abs/1503.07307 · HTML: https://mlsanity.com/paper/1503.07307/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2015.

## Built on by (most cited first, 2 of 2)

- [Fast marginal likelihood estimation of penalties for group-adaptive elastic net](https://mlsanity.com/paper/2101.03875/) (2021)
- [Corrected Integrated Laplace Approximation for Bayesian Inference in Latent Gaussian Models](https://mlsanity.com/paper/2605.20345/) (2026)

## Abstract (arXiv)

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.