prior_belief_ggm function

Prior Belief Gaussian Graphical Model

Incorporate prior information into the estimation of the conditional dependence structure. This prior information is expressed as the prior odds that each relation should be included in the graph.

prior_belief_ggm(Y, prior_ggm, post_odds_cut = 3, ...)

Arguments

• Y: Matrix (or data frame) of dimensions n (observations) by p (variables/nodes).
• prior_ggm: Matrix of dimensions p by p, encoding the prior odds for including each relation in the graph (see 'Details')
• post_odds_cut: Numeric. Threshold for including an edge (defaults to 3). Note post_odds refers to posterior odds.
• ...: Additional arguments passed to explore.

Returns

An object including:

• adj: Adjacency matrix
• post_prob: Posterior probability for the alternative hypothesis.

Details

Technically, the prior odds is not for including an edge in the graph, but for (H1)/p(H0), where H1 captures the hypothesized edge size and H0 is the null model \insertCite @see Williams2019_bfBGGM. Accordingly, setting an entry in prior_ggm to, say, 10, encodes a prior belief that H1 is 10 times more likely than H0. Further, setting an entry in prior_ggm to 1 results in equal prior odds (the default in select.explore).

Examples

# Assume perfect prior information
# synthetic ggm
p <- 20
main <- gen_net()

# prior odds 10:1, assuming graph is known
prior_ggm <- ifelse(main$adj == 1, 10, 1)

# generate data
y <- MASS::mvrnorm(n = 200,
                   mu = rep(0, 20),
                   Sigma = main$cors)

# prior est
prior_est <- prior_belief_ggm(Y = y,
                              prior_ggm = prior_ggm,
                              progress = FALSE)

# check scores
BGGM:::performance(Estimate = prior_est$adj,
                   True = main$adj)

# default in BGGM
default_est <- select(explore(y, progress = FALSE))

# check scores
BGGM:::performance(Estimate = default_est$Adj_10,
                   True = main$adj)