# Bayesian Computing with INLA: A Review

arXiv: https://arxiv.org/abs/1604.00860 · HTML: https://mlsanity.com/paper/1604.00860/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2016.

## Built on by (most cited first, 16 of 16)

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## Abstract (arXiv)

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.