Julia INLA Ecosystem

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

Status

v0.1.0-rc1. Phase A through D of the replan have landed: the four src/-bearing packages (GMRFs.jl, LatentGaussianModels.jl, INLASPDE.jl, INLASPDERasters.jl) cover the canonical R-INLA datasets — Scotland and Pennsylvania BYM2, Meuse zinc SPDE, the synthetic Negative Binomial / Gamma / Generic / Seasonal / Leroux / disconnected-Besag suite — within the testing strategy's tolerances. LGMTuring.jl provides the NUTS bridge for INLA-vs-MCMC triangulation.

What's here

• Getting started
• • A toy Poisson + IID model
  • Build the model
  • Fit by INLA
  • What's in the result
• Areal — Scotland lip-cancer BYM2
• • Loading the fixture
  • Building the model
  • Fitting
  • Posterior summaries
  • Comparing to R-INLA
  • Same model, written with @lgm
• Temporal — Tokyo rainfall (cyclic RW2 + Bernoulli)
• • Synthetic day-of-year series
  • Building the model
  • Fitting
  • Posterior summaries
  • Why the cyclic flag matters
  • Same model, written with @lgm
• Spatial — Meuse zinc SPDE
• • Loading the fixture
  • Building the model
  • Fitting
  • Posterior summaries
  • Comparing to R-INLA
  • Mesh parity (M3)
  • Predicting on a raster grid
  • Coming from R-INLA: the @lgm macro
• Survival — Cox PH and Weibull on synthetic data
• • Cox proportional hazards
  • Weibull survival
  • Picking a parameterisation
• Joint longitudinal + survival via Copy
• • Model
  • Simulate
  • Build the model
  • Fit
  • Fixed effects
  • Random-effect recovery
  • Hyperparameter recovery
  • Notes on extending the model
• GMRFs.jl
• • What's here
  • Required methods for new GMRF subtypes
  • API
• LatentGaussianModels.jl
• • What's here
  • Building a model
  • Component contract
  • API
• INLASPDE.jl
• • What's here
  • Required correctness tests
  • API
• INLASPDERasters.jl
• • What's here
  • Why a sub-package, not a weakdep
  • API
• References
• • Method papers
  • Validation datasets
  • Where we differ from R-INLA

Installing

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

To install only one core package, substitute "INLA" for "GMRFs", "LatentGaussianModels", "INLASPDE", or "INLASPDERasters".

Optional sub-packages (LGMTuring.jl, LGMFormula.jl, GMRFsPardiso.jl) are not registered yet — install them by Pkg.develop-ing this repo's subdir directly, e.g.

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

How to read this site

• Getting started — the smallest possible Poisson + spatial random effect fit, top to bottom.
• Coming from R-INLA → Migration guide — side-by-side reference: every R-INLA family, f(model = ...), prior, integration strategy, and post-fit accessor mapped to its Julia constructor or accessor function. Open this next to your R script while translating.
• Coming from R-INLA → Formula DSL (@lgm) — if your R-INLA workflow leans on the formula DSL, the @lgm macro in LGMFormula.jl provides a near-source-to-source migration path. Worked examples for Scotland BYM2 and beyond.
• Vignettes — five end-to-end walkthroughs:
  • Scotland BYM2 (areal Poisson with BYM2 spatial random effect),
  • Tokyo rainfall (Bernoulli with a cyclic RW2 seasonal),
  • Meuse zinc SPDE (Gaussian on point-referenced data via the SPDE–Matérn link),
  • CoxPH and Weibull survival (right-censored time-to-event regression with the augmented piecewise-exponential and PH-Weibull pathways),
  • Joint longitudinal + survival (Baghfalaki-style multi-likelihood model with Copy-shared subject random effect).
• Packages — per-package overviews, exported API, and required contracts for extending them.
• References — the canonical method papers and validation datasets we test against.

Differences from R-INLA

A side-by-side surface map for every R-INLA construct currently covered (likelihoods, components, priors, accessors, prediction, sampling) lives in Coming from R-INLA → Migration guide. The full list of default-parameter parity calls lives in plans/defaults-parity.md. Highlights:

• Single dispatch table. Every latent component, likelihood, prior, and integration scheme is a struct + a handful of methods. Adding a new component is "subtype AbstractLatentComponent and implement five methods" — no formula-DSL gatekeeping.
• LogDensityProblems seam. The posterior is a LogDensityProblems-conformant object; downstream samplers (Turing, AdvancedHMC, custom) plug in without touching this package.
• R-INLA-equivalent BYM2 scaling and PC priors by default. Where we differ, the docstring says so.
• No f(...) / inla.formula macro magic. A formula sugar layer (@lgm) exists in LGMFormula.jl for users coming from R; the underlying constructor API is the source of truth.