GMRFs in JuliaFast and Flexible Latent Gaussian Modelling

Clean syntax, fast computations. Powered by the Julia ecosystem.

⚡ High Performance

Leverages sparse matrix structures for fast computations, enabled by LinearSolve.jl and SelectedInversion.jl.

📊 Smart Observation Models

Built-in exponential family support. Sparse autodiff makes it easy to define your own likelihoods.

🎯 Ready-to-Use Latent Models

AR1, RW1, Besag, ... out-of-the-box. Combine them seamlessly to build complex hierarchical structures.

🔬 SPDE Discretizations

Model with a GP, compute with a GMRF. The SPDE approach makes it possible.

🧮 Solver Variety

CHOLMOD, Pardiso, Krylov methods... Your choice - we make it work.

🔗 Composable Design

Mix and match components: combine latent models, stack observation models, chain transformations - everything just works together.

What are Gaussian Markov Random Fields?

Gaussian Markov Random Fields (GMRFs) are Gaussian distributions with sparse precision (inverse covariance) matrices. This sparsity structure makes them computationally efficient for large-scale problems while maintaining the expressiveness needed for complex spatial and temporal modeling.

Quick Start

Install the package:

julia

using Pkg
Pkg.add("GaussianMarkovRandomFields")
using GaussianMarkovRandomFields