get_MPMdag {BCDAG}R Documentation

Compute the median probability DAG model from the MCMC output


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





object of class bcdag


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.


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


Federico Castelletti and Alessandro Mascaro


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


# Randomly generate a DAG and the DAG-parameters
q = 8
w = 0.2
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

[Package BCDAG version 1.0.0 Index]