Mixture of Directed Graphical Models • mdgm

Full documentation: https://jbcart.github.io/mdgm/

mdgm (Mixture of Directed Graphical Models) provides Bayesian inference for discrete spatial random fields. Instead of working with a Markov random field and its intractable normalizing constant, the MDGM defines a mixture over directed acyclic graphs (DAGs) compatible with an undirected neighborhood graph. Each DAG admits a tractable likelihood, avoiding the partition function entirely.

See Carter and Calder (2024) for the full methodological details.

Installation

You can install the development version from GitHub:

# install.packages("pak")
pak::pak("jbcart/mdgm")

A C++20 compiler is required.

Quick start

library(mdgm)

# Build a 4x4 grid graph with rook adjacency
nug <- nug_from_grid(4, 4, seed = 42L)
nug$nvertices()
#> [1] 16
nug$nedges()
#> [1] 24

# Fit a standalone spanning-tree MDGM
z <- c(0L, 0L, 0L, 1L,
       0L, 0L, 1L, 1L,
       1L, 1L, 1L, 0L,
       1L, 1L, 0L, 0L)
model <- mdgm_model(nug, dag_type = "spanning_tree")
result <- mcmc(model, z_init = z, psi_init = 0.5,
               n_iter = 2000L, psi_tune = 1.0, seed = 42L)
result$summary()
#> MDGM MCMC Results
#>   Vertices: 16, Colors: 2
#>   Iterations: 2000 (burnin: 0)
#>   Psi acceptance rate: 0.462
#>   Psi posterior mean: 0.8447 (sd: 0.5658)
#>   Psi R-hat: 1.0035, ESS: 308

See vignette("mdgm") for a full walkthrough including visualization and posterior diagnostics.

C++ unit tests

The C++ core ships with GoogleTest unit tests under tests/cpp/. Build and run them with:

cmake -B build -DBUILD_TESTS=ON
cmake --build build
ctest --test-dir build