get_diagnostics {BCDAG}

MCMC diagnostics

Description

This function provides diagnostics of convergence for the MCMC output of learn_DAG function.

Usage

get_diagnostics(learnDAG_output, ask = TRUE, nodes = integer(0))

Arguments

learnDAG_output

object of class bcdag

ask

Boolean argument passed to par() for visualization;

nodes

Numerical vector indicating those nodes for which we want to compute the posterior probability of edge inclusion;

Details

Function learn_DAG implements a Markov Chain Monte Carlo (MCMC) algorithm for structure learning and posterior inference of Gaussian DAGs. Output of the algorithm is a collection of S DAG structures (represented as (q,q) adjacency matrices) and DAG parameters (D,L) approximately drawn from the joint posterior. In addition, if learn_DAG is implemented with collapse = TRUE, the only approximate marginal posterior of DAGs (represented by the collection of S DAG structures) is returned; see the documentation of learn_DAG for more details.

Diagnostics of convergence for the MCMC output are conducted by monitoring across MCMC iterations: (1) the number of edges in the DAGs; (2) the posterior probability of edge inclusion for each possible edge u -> v. With regard to (1), a traceplot of the number of edges in the DAGs visited by the MCMC chain at each step s = 1, ..., S is first provided as the output of the function. The absence of trends in the plot can provide information on a genuine convergence of the MCMC chain. In addition, the traceplot of the average number of edges in the DAGs visited up to time s, for s = 1, ..., S, is also returned. The convergence of the curve around a "stable" average size generally suggests good convergence of the algorithm. With regard to (2), for each edge u -> v, the posterior probability at time s, for s = 1, ..., S, can be estimated as as the proportion of DAGs visited by the MCMC up to time s which contain the directed edge u -> v. Output is organized in q plots (one for each node v = 1, ..., q), each summarizing the posterior probabilities of edges u -> v, u = 1, ..., q. If the number of nodes is larger than 30 the traceplot of a random sample of 30 nodes is returned.

Value

A collection of plots summarizing the behavior of the number of edges and the posterior probabilities of edge inclusion computed from the MCMC output.

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.

F. Castelletti (2020). Bayesian model selection of Gaussian Directed Acyclic Graph structures. International Statistical Review 88 752-775.

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)
n = 200
# Generate observations from a Gaussian DAG-model
X = mvtnorm::rmvnorm(n = n, sigma = Sigma)
# Run the MCMC for posterior inference of DAGs only (collapse = TRUE)
out_mcmc = learn_DAG(S = 5000, burn = 1000, a = q, U = diag(1,q)/n, data = X, w = 0.1,
                                   fast = TRUE, save.memory = FALSE, collapse = TRUE)
# Produce diagnostic plots
get_diagnostics(out_mcmc)