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GMRFs.jl

Sparse Gaussian Markov Random Fields for Julia.

A standalone, dependency-light package providing:

  • AbstractGMRF and concrete types for IID, random-walk, AR(1), seasonal, Besag, and Generic0 sparse-precision models.
  • GMRFGraph — Graphs.jl-compatible graph wrapping any sparse adjacency.
  • Sampling from N(μ, Q⁻¹) with and without linear constraints.
  • Log-density evaluation and log-determinant.
  • Marginal variances via selected inversion.
  • Sparse factorization caching (FactorCache) — symbolic-once, refactor-on-θ-change — exposed through LinearSolve.jl.

This package is the numerical core of the Julia INLA ecosystem but is usable independently for any application involving sparse Gaussian models: spatial smoothing, disease mapping with external MCMC, image restoration, 4D-Var data assimilation.

Status

v0.1.0-rc1. See the ecosystem CHANGELOG.md for what landed and where R-INLA parity is known to be loose.

Shipped concrete types: IIDGMRF, RW1GMRF, RW2GMRF, AR1GMRF, SeasonalGMRF, BesagGMRF, Generic0GMRF.

Quick example

using GMRFs, Graphs, SparseArrays, Random

# Besag prior on a small adjacency. `GMRFGraph` accepts a
# `Graphs.AbstractGraph` or a sparse adjacency matrix.
g = GMRFGraph(cycle_graph(6))
prior = BesagGMRF(g; τ = 1.0, scale_model = true)

# Sample from the prior (linear sum-to-zero constraint applied).
x = rand(MersenneTwister(1), prior)

# Log-density
ℓ = logpdf(prior, x)

# Marginal variances diag(Q⁻¹) via selected inversion
σ² = marginal_variances(prior)

# Reuse the symbolic factor when only τ changes
cache = FactorCache(prior)
update!(cache, BesagGMRF(g; τ = 4.0, scale_model = true))

Installation

Registered on a personal Julia registry at haavardhvarnes/JuliaRegistry — add it once, then Pkg.add as usual:

using Pkg
Pkg.Registry.add(RegistrySpec(url = "https://github.com/haavardhvarnes/JuliaRegistry"))
Pkg.add("GMRFs")

See also