GMRFs.jl

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Formula Interface ​

The formula interface lets you compose models succinctly using StatsModels.jl syntax. It maps terms on the right-hand side to latent components and assembles a sparse design matrix that connects observations to the combined latent field. To use the formula syntax, load StatsModels first to activate the corresponding package extension.

Quick Example ​

julia
using GaussianMarkovRandomFields, StatsModels, Distributions, SparseArrays

# Suppose W is a spatial adjacency for regions; y are counts with an offset
besag = Besag(W)                         # structured spatial effect
f = @formula(y ~ 1 + x + IID(region) + besag(region))
comp = build_formula_components(f, data; family = Poisson)
lik  = comp.obs_model(data.y; offset = data.logE)
prior = comp.combined_model(; τ_besag=1.0, τ_iid=1.0)
post  = gaussian_approximation(prior, lik)

Terms and Builders ​

GaussianMarkovRandomFields.IID Function
julia
IID(group)

Formula constructor for IID random effects. Use only inside @formula.

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GaussianMarkovRandomFields.RandomWalk Function
julia
RandomWalk(order, index)

Formula constructor for RandomWalk random effects (order=1 MVP). Use only inside @formula.

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GaussianMarkovRandomFields.AR1 Function
julia
AR1(index)

Formula constructor for AR1 random effects. Use only inside @formula.

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GaussianMarkovRandomFields.Besag Type
julia
Besag(W; id_to_node = nothing, normalize_var = true, singleton_policy = :gaussian)

Formula functor for Besag (intrinsic CAR) random effects.

Usage:

  • Create a functor instance: besag = Besag(W)

  • With string/categorical region IDs: besag = Besag(W; id_to_node = Dict("WesternIsles" => 11, ...))

  • Use in a formula: @formula(y ~ 0 + besag(region))

Notes

  • id_to_node maps arbitrary region identifiers to integer node indices (1-based) of W.

  • Calling the functor directly is unsupported outside formula parsing.

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GaussianMarkovRandomFields.build_formula_components Function
julia
build_formula_components(formula, data; kwargs...)

Placeholder function for the formula interface. A concrete method is provided by the GaussianMarkovRandomFieldsFormula extension when StatsModels is loaded.

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See Also ​