Integrated Nested Laplace Approximation

July 27, 2021 — July 26, 2022

Bayes
feature construction
machine learning
Monte Carlo
probabilistic algorithms
probability
signal processing
state space models
statistics

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Figure 1

Integrated nested Laplace approximation (Rue, Martino, and Chopin 2009, 2009; Ingebrigtsen, Lindgren, and Steinsland 2014; Lindgren and Rue 2015; Rue et al. 2016) connects to the GP-as-SDE idea, I think? TBC.

1 References

Bakka, Rue, Fuglstad, et al. 2018. “Spatial Modeling with R-INLA: A Review.” WIREs Computational Statistics.
Dowling, Sokół, and Park. 2021. “Hida-Matérn Kernel.”
Ingebrigtsen, Lindgren, and Steinsland. 2014. “Spatial Models with Explanatory Variables in the Dependence Structure.” Spatial Statistics, Spatial Statistics Miami,.
Lindgren, and Rue. 2015. “Bayesian Spatial Modelling with R-INLA.” Journal of Statistical Software.
Miller, Glennie, and Seaton. 2020. “Understanding the Stochastic Partial Differential Equation Approach to Smoothing.” Journal of Agricultural, Biological and Environmental Statistics.
Opitz, Huser, Bakka, et al. 2018. “INLA Goes Extreme: Bayesian Tail Regression for the Estimation of High Spatio-Temporal Quantiles.” Extremes.
Rue, Martino, and Chopin. 2009. “Approximate Bayesian Inference for Latent Gaussian Models by Using Integrated Nested Laplace Approximations.” Journal of the Royal Statistical Society: Series B (Statistical Methodology).
Rue, Riebler, Sørbye, et al. 2016. “Bayesian Computing with INLA: A Review.” arXiv:1604.00860 [Stat].