mb: Compute the Markov blanket

In abn: Modelling Multivariate Data with Additive Bayesian Networks

Compute the Markov blanket

Description

This function computes the Markov blanket of a set of nodes given a DAG (Directed Acyclic Graph).

Usage

mb(dag, node, data.dists = NULL, data.df = NULL)

Arguments

dag	a matrix or a formula statement (see details for format) defining the network structure, a directed acyclic graph (DAG).
node	a character vector of the nodes for which the Markov Blanket should be returned.
data.dists	a named list giving the distribution for each node in the network, see details.
data.df	a data frame containing the data for the nodes in the network. Only needed if dag is a formula statement.

Details

This function returns the Markov Blanket of a set of nodes given a DAG.

The dag can be provided as a matrix where the rows and columns are the nodes names. The matrix should be binary, where 1 indicates an edge from the column node (parent) to the row node (child). The diagonal of the matrix should be 0 and the matrix should be acyclic. The nodes names should be the same as the names of the distributions in data.dists.

Alternatively, the dag can be provided using a formula statement (similar to glm). This requires the data.dists and data.df arguments to be provided. A typical formula is ~ node1|parent1:parent2 + node2:node3|parent3. The formula statement have to start with ~. In this example, node1 has two parents (parent1 and parent2). node2 and node3 are children of the same parent (parent3). The parents names have to exactly match those given in name. : is the separator between either children or parents, | separates children (left side) and parents (right side), + separates terms, . replaces all the variables in name.

Value

character vector of node names from the Markov blanket.

Examples

## Defining distribution and dag
dist <- list(a="gaussian", b="gaussian", c="gaussian", d="gaussian",
             e="binomial", f="binomial")
dag <- matrix(c(0,1,1,0,1,0,
                0,0,1,1,0,1,
                0,0,0,0,0,0,
                0,0,0,0,0,0,
                0,0,0,0,0,1,
                0,0,0,0,0,0), nrow = 6L, ncol = 6L, byrow = TRUE)
colnames(dag) <- rownames(dag) <- names(dist)

mb(dag, node = "b", data.dists = dist)
mb(dag, node = c("b","e"), data.dists = dist)

abn documentation built on June 8, 2025, 10:53 a.m.