mdgm: Mixture of Directed Graphical Models

Bayesian inference for discrete spatial random fields using mixtures of directed graphical models (MDGM). The package provides MCMC sampling over directed acyclic graph (DAG) structures—including spanning trees and acyclic orientations—with optional emission models for hierarchical observation processes.

Creates a configuration object for a mixture of directed graphical models spatial field. Used as the spatial argument to srf_model().

Usage

mdgm(dag_type = c("spanning_tree", "acyclic_orientation", "rooted"))

Arguments

dag_type: DAG construction type: "spanning_tree", "acyclic_orientation", or "rooted".

Value

A list of class mdgm_config.

Model types

Standalone: The spatial field \(z\) is observed directly. The MCMC updates the DAG structure and dependence parameter \(\psi\).
Hierarchical: A latent spatial field \(z\) generates observations \(y\) through an emission distribution (e.g., Bernoulli). The MCMC additionally updates \(z\) and emission parameters.

Key functions

Graph construction: nug_from_edge_list(), nug_from_adj_list(), nug_from_adj_mat()
Model specification: srf_model() with mdgm() or mrf() configuration helpers
MCMC inference: mcmc()

References

Carter, J. B. and Calder, C. A. (2024). Mixture of Directed Graphical Models for Discrete Spatial Random Fields. doi:10.48550/arXiv.2406.15700

Author

Maintainer: Brandon Carter brandon.carter@duke.edu

Examples

mdgm(dag_type = "spanning_tree")
#> $dag_type
#> [1] "spanning_tree"
#> 
#> attr(,"class")
#> [1] "mdgm_config"