Bayesian Computing with INLA: A Review

By Håvard Rue, Andrea Riebler, Sigrunn Holbek Sørbye, J. Illian, Daniel P. Simpson, Finn Lindgren. 2016

746 citations recorded by the source corpus.

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 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.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/94c449d8e6813fe7d47c97096535b7696bbaef8b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

Spatial modelling with R-INLA: A review (2018, methodology): “In this section we give a brief overview of the parts central to spatial models from the R-INLA review paper (Rue et al., 2017).”
Projecting the future burden of cancer: Bayesian age–period–cohort analysis with integrated nested Laplace approximations (2017, methodology): “Integrated nested Laplace approximations (INLA) (Rue et al., 2009, 2016) have been shown to be useful to perform MCMC-free inference in APC models (Riebler et al., 2012a) and other Bayesian hierarchical models (Schrödle and Held, 2011; Schrödle et al., 2011).”
Accounting for individual-specific variation in habitat-selection studies: Efficient estimation of mixed-effects models using Bayesian or frequentist computation (2018, background): “Efficiency thus strongly depends the number of hyperparameters, and it should not exceed 20 (Rue et al., 2016).”
INLA goes extreme: Bayesian tail regression for the estimation of high spatio-temporal quantiles (2018, methodology): “…inference approach relies on the Integrated Nested Laplace Approx-2 imation (INLA) of posterior distributions, which is much faster and sidesteps convergence issues in simulation-based techniques, while providing highly accurate results (Rue et al. , 2009; Martins et al. , 2013; Rue et al. , 2017).”
Spatiotemporal wildfire modeling through point processes with moderate and extreme marks (2021, methodology): “With the R-INLA implementation (Rue et al. 2017), up to several hundred thousand observations can be handled.”
Validating Bayesian Inference Algorithms with Simulation-Based Calibration (2018, methodology): “…but also deterministic methods that yield approximate posterior distributions amenable to exact sampling, such as integrated nested Laplace approximation (INLA) (Rue, Martino and Chopin, 2009; Rue et al., 2017) and automatic diﬀerentiation variational inference (ADVI) (Kucukelbir et al., 2017).”
Maximum likelihood estimation of spatially varying coefficient models for large data with an application to real estate price prediction (2020, background): “A drawback of INLA is the critical assumption on the number of hyperparameters that one can estimate which should be ‘‘small, typically 2 to 5, but not exceeding 20’’ (Rue et al., 2017) and therefore the number of SVCs in a model is limited.”
Geostatistical Modeling to Capture Seismic‐Shaking Patterns From Earthquake‐Induced Landslides (2018, background): “A general review of INLA can be found in Rue et al. (2017), while a more detailed review of spatial modeling can be found in Bakka et al. (2018).”