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References — annotated bibliography

Key papers and books for the port. Grouped by role in the project.

Method foundation (read first)

Rue, H., Martino, S., & Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. JRSS-B, 71(2), 319–392.

The INLA paper. Defines latent Gaussian models, the Laplace approximation scheme, CCD for hyperparameter integration. Read §2–3 for the spine of the algorithm.

Lindgren, F., Rue, H., & Lindström, J. (2011). An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach. JRSS-B, 73(4), 423–498.

SPDE. The Matérn–GMRF link via Hilbert space projection. §2–4 are the theory; §5 gives the FEM matrices you need to reproduce (C, G₁, G₂).

Lindgren, F., & Rue, H. (2015). Bayesian Spatial Modelling with R-INLA. Journal of Statistical Software, 63(19).

The R-INLA SPDE interface paper. Reference for how the API was shaped.

Lindgren, F., Bolin, D., & Rue, H. (2022). The SPDE approach for Gaussian and non-Gaussian fields: 10 years and still running. Spatial Statistics, 50, 100599.

The review of the SPDE approach. §4 covers non-stationarity and non-Gaussian extensions we probably won't implement in v1 but must understand to avoid painting ourselves into a corner.

Priors and parameterization

Simpson, D., Rue, H., Riebler, A., Martins, T., & Sørbye, S. (2017). Penalising model component complexity: A principled, practical approach to constructing priors. Statistical Science, 32(1), 1–28.

PC priors. This defines the prior parameterization used for precisions, ranges, and mixing parameters throughout R-INLA. Required reading.

Fuglstad, G.-A., Simpson, D., Lindgren, F., & Rue, H. (2019). Constructing priors that penalize the complexity of Gaussian random fields. JASA, 114(525), 445–452.

PC priors specifically for SPDE–Matérn (range and σ). Phase 4 deliverable.

Sørbye, S. H., & Rue, H. (2014). Scaling intrinsic Gaussian Markov random field priors in spatial modelling. Spatial Statistics, 8, 39–51.

Why and how to scale intrinsic GMRFs. scale.model = TRUE comes from here. Hyperparameter interpretability across graphs depends on this.

Riebler, A., Sørbye, S. H., Simpson, D., & Rue, H. (2016). An intuitive Bayesian spatial model for disease mapping that accounts for scaling. SMMR, 25(4), 1145–1165.

BYM2. The reparameterization that cleaned up BYM's identifiability issues. Our Phase 2 headline model.

Freni-Sterrantino, A., Ventrucci, M., & Rue, H. (2018). A note on intrinsic conditional autoregressive models for disconnected graphs. SSTE, 26, 25–34.

The disconnected-components fix. Without this you silently compute wrong posteriors on graphs with islands/isolated nodes.

Algorithmic & computational

Martins, T. G., Simpson, D., Lindgren, F., & Rue, H. (2013). Bayesian computing with INLA: New features. CSDA, 67, 68–83.

The PC prior case studies, the control.mode and copy mechanism, multiple likelihoods. Useful for understanding R-INLA's feature surface.

Lindgren, F., Bakka, H., Bolin, D., Krainski, E., & Rue, H. (2024). A diffusion-based spatio-temporal extension of Gaussian Matérn fields. SORT, 48(1), 3–66.

Non-separable space-time SPDEs. Phase 5/6.

Bolin, D., & Kirchner, K. (2020). The rational SPDE approach for Gaussian random fields with general smoothness. JCGS, 29(2), 274–285.

Fractional-α SPDE via rational approximations. Phase 6 optimization.

Van Niekerk, J., Krainski, E., Rustand, D., & Rue, H. (2023). A new avenue for Bayesian inference with INLA. CSDA, 181, 107692.

Recent developments in the INLA algorithm itself, including the current parallelization scheme. Useful to know before Phase 6 perf work.

Textbooks (validation oracles)

Moraga, P. (2024). Geospatial Health Data: Modeling and Visualization with R-INLA and Shiny (2nd ed.). Chapman & Hall/CRC.

Phase 4 tier-4 test suite. Every chapter is implicitly a regression test. Code online.

Blangiardo, M., & Cameletti, M. (2015). Spatial and Spatio-Temporal Bayesian Models with R-INLA. Wiley.

The canonical textbook. Datasets and code online.

Gómez-Rubio, V. (2020). Bayesian Inference with INLA. Chapman & Hall/CRC.

More advanced: INLA-within-MCMC, missing data, mixture models. Many useful test cases for Phase 5.

Krainski, E. T., Gómez-Rubio, V., Bakka, H., Lenzi, A., Castro-Camilo, D., Simpson, D., Lindgren, F., & Rue, H. (2019). Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA. Chapman & Hall/CRC.

SPDE cookbook. Phase 4 reference.

Code references

  • hrue/r-inla — the reference implementation.
    • gmrflib/ for the sparse GMRF core
    • inlaprog/ for the INLA loop
    • fmesher/ for meshing
    • rinla/R/ for the R wrapper layer (model definitions, formula parsing)
  • hrue/r-inla-testing — developer scratch tests.
  • spatialstatisticsupna/Comparing-R-INLA-and-NIMBLE — NIMBLE cross-checks.
  • ConnorDonegan/Stan-IAR — Stan ICAR/BYM/BYM2 implementations.
  • inlabru-org/fmesher — Lindgren's standalone C++ meshing (cleaner than the version inside r-inla).

Related Julia packages (for interop and comparison)

  • JuliaGaussianProcesses/AbstractGPs.jl — GP infrastructure, dense.
  • JuliaEarth/GeoStats.jl — classical geostatistics, Meshes.jl-based.
  • SciML/NonlinearSolve.jl, LinearSolve.jl, Optimization.jl.
  • TuringLang/Turing.jl — downstream bridge via LogDensityProblems.
  • rafaqz/Rasters.jl — gridded covariates and prediction surfaces.