A collection of extended Gaussian Markov Random Field models for Bayesian spatial and spatio-temporal inference, implemented within the INLA framework.
Each model extends a classical GMRF to capture richer spatial structure,
implemented via the INLA cgeneric interface for efficient Bayesian inference.
Flexible extension of the BYM2 model, combining structured (ICAR) and unstructured (iid) spatial effects with sub-region-varying precision parameters. Inherits the interpretability and scaling properties of BYM2 while relaxing the stationarity assumption.
Stacked block-diagonal GMRF on latent dim p × n.
Precision is diag(exp(θ1) R1, …, exp(θp) Rp),
so each of the p blocks runs independently with its
own precision matrix and log-precision hyperparameter.
Collapsed multi-block GMRF: p dense covariance
matrices combined into a single latent effect of size
n with covariance
Σ(θ) = ∑j exp(−θj) Gj.
Each block carries its own log-precision, enabling adaptive
weighting of competing covariance structures within one effect.
Partial split GMRF on latent dim 2n: the chosen
block is separated with its own precision
exp(θ1) R1, while the
remaining p − 1 covariances are collapsed
into a single pooled second block. Useful when one component
should keep its distinct structure and the rest can share scale.
These models open new directions in non-stationary spatial modeling and flexible Bayesian inference. If you are interested in collaborating on methodology, applications, or software development, I would love to hear from you.
Statistics Program, CEMSE Division
King Abdullah University of Science and Technology (KAUST)