INLA Publications

Pre-INLA proof-of-concept and sparse inverse discussion

H. Rue and S. Martino. Approximate Bayesian inference for hierarchical Gaussian Markov random fields models. Journal of Statistical Planning and Inference, 137(10):3177–3192, 2007. Special Issue: Bayesian Inference for Stochastic Processes.

Main INLA paper

H. Rue, S. Martino, and N. Chopin. Approximate Bayesian inference for latent Gaussian models using integrated nested Laplace approximations (with discussion). Journal of the Royal Statistical Society, Series B, 71(2):319–392, 2009.

Follow-up methodology developments

T. G. Martins, D. Simpson, F. Lindgren, and H. Rue. Bayesian computing with INLA: New features. Computational Statistics & Data Analysis, 67:68–83, 2013.

Comprehensive INLA review

H. Rue, A. Riebler, S. H. Sørbye, J. B. Illian, D. P. Simpson, and F. K. Lindgren. Bayesian computing with INLA: A review. Annual Reviews of Statistics and Its Applications, 4(March):395–421, 2017. doi:10.1146/annurev-statistics-060116-054045.

INLA 2.0 papers

J. van Niekerk, E. Krainksi, D. Rustand, and H. Rue. A new avenue for Bayesian inference with INLA. Computational Statistics & Data Analysis, 181:107692, May 2023. doi:10.1016/j.csda.2023.107692.

J. van Niekerk, H. Bakka, H. Rue, and O. Schenk. New frontiers in Bayesian modeling using the INLA package in R. Journal of Statistical Software, 100(2):1–28, 2021. doi:10.18637/jss.v100.i02.

VB mean correction in INLA 2.0

J. van Niekerk and H. Rue. Low-rank variational Bayes correction to the Laplace method. Journal of Machine Learning Research, 25(62):1–25, 2024. https://jmlr.org/papers/v25/21-1405.html.

Parallelisation strategies in INLA

L. Gaedke-Merzhäuser, J. van Niekerk, O. Schenk, and H. Rue. Parallelized integrated nested laplace approximations for fast Bayesian inference. Statistics and Computing, 33(1), 2022. doi:10.1007/s11222-022-10192-1.

R. S. Bivand, V. Gómez-Rubio, and H. Rue. Spatial data analysis with R-INLA with some extensions. Journal of Statistical Software, 63(20):1–31, 2015.

F. Lindgren and H. Rue. Bayesian spatial modelling with R-INLA. Journal of Statistical Software, 63(19):1–25, 2015.

T. D. Meehan, N. L. Michel, and H. Rue. Estimating animal abundance with N-mixture models using the R-INLA package for R. Journal of Statistical Software, 95(2):10016, 2020. doi:10.18637/jss.v095.i02.

J. van Niekerk, H. Bakka, H. Rue, and O. Schenk. New frontiers in Bayesian modeling using the INLA package in R. Journal of Statistical Software, 100(2):1–28, 2021. doi:10.18637/jss.v100.i02.