get_MPMdag {BCDAG}

Compute the median probability DAG model from the MCMC output

Description

This function computes the Median Probability DAG Model estimate (MPM) from the MCMC output of learn_DAG

Usage

get_MPMdag(learnDAG_output)

Arguments

learnDAG_output

object of class bcdag

Details

Output of learn_dag function consists of S draws from the joint posterior of DAGs and DAG-parameters in a zero-mean Gaussian DAG-model; see the documentation of learn_DAG for more details.

The Median Probability DAG Model estimate (MPM) is obtained by including all edges whose posterior probability exceeds 0.5. The posterior probability of inclusion of u -> v is estimated as the frequency of DAGs visited by the MCMC which contain the directed edge u -> v; see also function get_edgeprobs and the corresponding documentation.

Value

The (q,q) adjacency matrix of the median probability DAG model

Author(s)

Federico Castelletti and Alessandro Mascaro

References

F. Castelletti and A. Mascaro (2021). Structural learning and estimation of joint causal effects among network-dependent variables. Statistical Methods and Applications, Advance publication

M.M. Barbieri and J.O. Berger (2004). Optimal predictive model selection. The Annals of Statistics 32 870-897

Examples

# Randomly generate a DAG and the DAG-parameters
q = 8
w = 0.2
set.seed(123)
DAG = rDAG(q = q, w = w)
outDL = rDAGWishart(n = 1, DAG = DAG, a = q, U = diag(1, q))
L = outDL$L; D = outDL$D
Sigma = solve(t(L))%*%D%*%solve(L)
# Generate observations from a Gaussian DAG-model
n = 200
X = mvtnorm::rmvnorm(n = n, sigma = Sigma)
# Run the MCMC (Set S = 5000 and burn = 1000 for better results)
out_mcmc = learn_DAG(S = 500, burn = 100, a = q, U = diag(1,q)/n, data = X, w = 0.1,
                     fast = TRUE, save.memory = FALSE)
# Produce the MPM DAG estimate
get_MPMdag(out_mcmc)