graphicalExtremes (version 0.1.0)

complete_Gamma: Completion of Gamma matrix on block graphs

Description

Given a block graph and Gamma matrix with entries only specified on edges within the cliques of the graph, it returns the full Gamma matrix implied by the conditional independencies.

Usage

complete_Gamma(Gamma, graph)

Value

Completed \(d \times d\)

Gamma matrix. s

Arguments

Gamma

Numeric \(d \times d\) variogram matrix with entries only specified within the cliques of the graph. Alternatively, can be a vector containing the Gamma entries for each edge in the same order as in the graph object.

graph

Graph object from igraph package. The graph must be an undirected block graph, i.e., a decomposable, connected graph with singleton separator sets.

Details

For a block graph it suffices to specify the dependence parameters of the Huesler--Reiss distribution within the cliques of the graph, the remaining entries are implied by the conditional independence properties. For details see eng2019;textualgraphicalExtremes.

References

Examples

## Complete a 4-dimensional HR distribution

my_graph <- igraph::graph_from_adjacency_matrix(rbind(
c(0, 1, 0, 0),
c(1, 0, 1, 1),
c(0, 1, 0, 1),
c(0, 1, 1, 0)),
mode = "undirected")

Gamma <- rbind(
c(0, .5, NA, NA),
c(.5, 0, 1, 1.5),
c(NA, 1, 0, .8),
c(NA, 1.5, .8, 0))

complete_Gamma(Gamma, my_graph)

## Alternative

Gamma_vec <- c(.5, 1, 1.5, .8)
complete_Gamma(Gamma_vec, my_graph)