Julia INLA Ecosystem

A Julia-native reimplementation of the latent Gaussian model / INLA stack originally provided by R-INLA. The goal is not line-by-line port but a composable, dispatch-based, SciML-aligned alternative that covers the mainstream use cases of R-INLA with native performance and genuine extensibility.

Status

v1.1.0. The src/-bearing packages (GMRFs.jl, LatentGaussianModels.jl, INLASPDE.jl, INLASPDERasters.jl, LGMFormula.jl, LGMTuring.jl) cover the canonical R-INLA datasets within the testing-strategy tolerances. See CHANGELOG.md for what landed and where R-INLA parity is known to be loose.

Packages

Core ecosystem

Package	Purpose	Depends on
GMRFs.jl	Sparse Gaussian Markov random fields: graph, precision, sampling, conditioning, log-density. Standalone-useful.	SparseArrays, LinearSolve, Graphs, Distributions, ChainRulesCore
LatentGaussianModels.jl	LGM abstraction, latent components (IID/RW/AR1/Besag/BYM2/…), likelihoods, INLA inference. LogDensityProblems seam for downstream samplers.	GMRFs, NonlinearSolve, Optimization, LogDensityProblems
INLASPDE.jl	SPDE–Matérn finite-element assembly on Meshes.jl triangulations.	LatentGaussianModels, Meshes, DelaunayTriangulation, CoordRefSystems

Optional sub-packages (install separately)

Heavy integrations live outside the core to keep load times small and release cadences independent. Install whichever you need.

Package	Purpose	Adds dep on
LGMFormula.jl	Tier-2 @lgm formula sugar over LatentGaussianModel(...).	StatsModels
LGMTuring.jl	HMC/NUTS bridge for cross-validation and INLA-within-MCMC flows.	Turing, AdvancedHMC
GMRFsPardiso.jl	MKL / Panua Pardiso factorization backend for GMRFs.jl. License-gated.	Pardiso
INLASPDERasters.jl	Covariate extraction from rasters + raster prediction surfaces.	Rasters

The umbrella package INLA.jl re-exports GMRFs, LatentGaussianModels, and INLASPDE so that using INLA brings the inference stack into scope in one import.

Installation

The packages are registered on a personal Julia registry at haavardhvarnes/JuliaRegistry. From a fresh Julia REPL:

using Pkg
Pkg.Registry.add(RegistrySpec(url = "https://github.com/haavardhvarnes/JuliaRegistry"))
Pkg.add("INLA")              # umbrella: GMRFs + LatentGaussianModels + INLASPDE

For a leaner install, replace "INLA" with any individual core package — "GMRFs", "LatentGaussianModels", "INLASPDE", or "INLASPDERasters". INLASPDERasters ships a working raster–SPDE bridge exercised end-to-end by the Meuse SPDE vignette; see its README.

The optional sub-packages LGMTuring.jl, LGMFormula.jl, and GMRFsPardiso.jl are not registered yet. Install them by Pkg.develop-ing this repo's subdir directly:

Pkg.develop(url = "https://github.com/haavardhvarnes/INLA.jl",
            subdir = "packages/LGMTuring.jl")

What ships in v1.1.0

• Latent components: Intercept, FixedEffects, IID, RW1, RW2, AR1, Seasonal, Besag, BYM, BYM2, Leroux, Generic0, Generic1, SPDE2 (α = 2 Matérn).
• Likelihoods: Gaussian, Poisson, Binomial, NegativeBinomial, Gamma — with closed-form gradients/Hessians for the inner Newton loop and a ForwardDiff fallback for user-defined cases.
• Hyperpriors: PCPrecision, GammaPrecision, LogNormalPrecision, WeakPrior, PCBYM2Phi, LogitBeta.
• Inference strategies: EmpiricalBayes (Laplace at θ̂), INLA (Laplace + θ-integration), and a LogDensityProblems seam for external samplers — LGMTuring.jl provides the NUTS bridge.
• θ-integration schemes: Grid, GaussHermite, CCD — int_strategy = :auto chooses CCD for dim θ > 2, Grid otherwise.
• Diagnostics: DIC, WAIC, CPO, PIT.
• Formula sugar (Phase N): LGMFormula.jl ships a Tier-2 @lgm macro for users coming from R-INLA's inla(formula, …) API — source-to-source over the explicit constructor; see the migration guide.

Reproducing R-INLA parity

Eleven R-INLA oracle fixtures (Scotland and Pennsylvania BYM2, classical BYM, synthetic Gamma / Negative Binomial / Generic0 / Generic1 / Seasonal / Leroux / disconnected Besag, Meuse SPDE) are checked into the test suite, each with the R-INLA posterior summaries and cpu.used wall-clock embedded.

The reproducer script at bench/oracle_compare.jl runs every problem end-to-end, prints a markdown table of relative errors and side-by-side wall-clock seconds, and writes the full per-quantity comparison to JSON. From the repo root:

julia --project=bench bench/oracle_compare.jl

See bench/README.md for column meanings, expected runtime (~3-5 minutes), and the JSON schema.

Directory map

• plans/ — ecosystem-level design documents (architecture, dependencies, testing, macro policy, ADR log).
• references/ — annotated bibliography and notes on upstream INLA source.
• bench/ — R-INLA parity reproducer (oracle_compare.jl) and its env.
• benchmarks/ — performance harness (run.jl) timing INLA.jl vs R-INLA on the flagship datasets; results in benchmarks/results/.
• docs/ — Documenter site source (docs/src/); built site lives at docs/build/ (gitignored).
• scripts/ — fixture generation and utilities.
• packages/ — the Julia packages themselves, each with its own plan and CLAUDE.md.

Working principles

See CLAUDE.md for the full set. Short version:

1. Multiple dispatch is the primary extension mechanism. Macros are optional sugar, never semantics.
2. Compose existing ecosystem packages rather than owning types — GeoInterface, Graphs, Meshes, Distributions, LinearSolve.
3. Validation against R-INLA on canonical datasets is a first-class test tier, not an afterthought.
4. SciML code style; weakdeps/extensions for optional integrations.

License

MIT (each package licensed independently, but all packages in the ecosystem use MIT).