References
The full annotated bibliography lives in references/papers.md; this page collects the load-bearing papers for users.
Method papers
- Rue, Martino & Chopin (2009), Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations, JRSS-B. The original INLA paper. The simplified Laplace, CCD integration, and skew-correction recipes all come from here.
- Rue & Held (2005), Gaussian Markov Random Fields. The book. GMRFs.jl is a partial Julia reimplementation of its numerical core.
- Lindgren, Rue & Lindström (2011), An explicit link between Gaussian fields and Gaussian Markov random fields: the SPDE approach, JRSS-B. The basis of
INLASPDE.jl. - Riebler et al. (2016), An intuitive Bayesian spatial model for disease mapping that accounts for scaling. The BYM2 parameterisation we use.
- Simpson, Rue, Riebler, Martins & Sørbye (2017), Penalising model component complexity: a principled, practical approach to constructing priors. PC priors throughout the ecosystem.
- Fuglstad, Simpson, Lindgren & Rue (2019), Constructing priors that penalize the complexity of Gaussian random fields. PC-Matérn prior on (range, σ).
- Freni-Sterrantino, Ventrucci & Rue (2018), A note on intrinsic conditional autoregressive models for disconnected graphs. The disconnected-graph sum-to-zero correction we apply to BYM, BYM2, and Besag.
Validation datasets
Each ships as a JLD2 fixture under packages/LatentGaussianModels.jl/test/oracle/fixtures/ or packages/INLASPDE.jl/test/oracle/fixtures/, generated by R scripts pinned to specific R-INLA versions in scripts/generate-fixtures/.
| Dataset | Used for |
|---|---|
Scotland lip cancer (scotland_bym2, scotland_bym) | BYM2 / BYM areal |
Pennsylvania lung cancer (pennsylvania_bym2) | BYM2 areal |
Sardinia (synthetic synthetic_disconnected_besag) | Disconnected ICAR |
Meuse zinc (meuse_spde) | SPDE / geostatistics |
| Tokyo rainfall | Cyclic RW2 + Bernoulli |
| Synthetic Gamma / NegBin / Generic / Seasonal / Leroux | Per-component oracles |
Where we differ from R-INLA
The full divergence list is in plans/defaults-parity.md.