2026-08-14 –, Room 5
Bayesian spatial modeling is critical across science, yet most practitioners are locked into R due to R-INLA.
We present a Julia ecosystem to change this: GaussianMarkovRandomFields.jl provides fast sparse precision-based inference via SPDE discretizations & more, while IntegratedNestedLaplace.jl brings the full INLA methodology to Julia with a familiar formula interface.
We demonstrate the ecosystem on spatial disease mapping, showing competitive results with R-INLA and native Julia advantages.
Bayesian spatial modeling underpins research across epidemiology, ecology, climate science, and the social sciences. The dominant tool for this is R-INLA, an R package implementing Integrated Nested Laplace Approximation for fast approximate Bayesian inference in latent Gaussian models. Despite its success, R-INLA effectively locks researchers into the R ecosystem - there has been no equivalent in Julia or Python.
This talk presents two packages that together bring this capability to Julia:
GaussianMarkovRandomFields.jl provides the sparse precision foundation. It constructs Gaussian Markov random fields e.g. via finite element discretizations of stochastic partial differential equations (SPDEs), turning dense covariance matrices into sparse precision matrices that scale to large-scale inference problems.
The package supports multiple solver backends via LinearSolve.jl, autodiff support, and integrates with Ferrite.jl for finite element assembly.
IntegratedNestedLaplace.jl (in development) implements the full INLA methodology on top of this foundation:
Gaussian approximation of the latent posterior, grid-based hyperparameter exploration with numerical integration, and Laplace-corrected marginals for the latent field, all in a formula-based interface familiar to R users.
The talk will walk through the ecosystem from theory to practice, culminating in a live demonstration of a complete nontrivial spatial analysis: specifying the model via a formula, fitting with INLA, and visualizing the results - all in Julia.
Tim Weiland is a PhD student in the Methods of Machine Learning group at the University of Tübingen, where he works on scalable probabilistic PDE solvers.
His research combines Bayesian inference, sparse linear algebra, and physics-informed priors to make uncertainty quantification practical for large-scale scientific computing problems.