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/.

DatasetUsed 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 rainfallCyclic RW2 + Bernoulli
Synthetic Gamma / NegBin / Generic / Seasonal / LerouxPer-component oracles

Where we differ from R-INLA

The full divergence list is in plans/defaults-parity.md.