This function consists of several sampling algorithms for Bayesian model determination in undirected graphical models based on mariginal pseudo-likelihood.
To speed up the computations, the birth-death MCMC sampling algorithms are implemented in parallel using OpenMP in C++.
bdgraph.mpl( data, n = NULL, method = "ggm", transfer = TRUE,
algorithm = "bdmcmc", iter = 5000, burnin = iter / 2,
g.prior = 0.2, g.start = "empty",
jump = NULL, alpha = 0.5, save = FALSE,
cores = NULL, operator = "or", verbose = TRUE )An object with S3 class "bdgraph" is returned:
upper triangular matrix which corresponds the estimated posterior probabilities of all possible links.
For the case "save = TRUE" is returned:
vector of strings which includes the adjacency matrices of visited graphs after burn-in.
vector which includes the waiting times of visited graphs after burn-in.
vector which includes the identity of the adjacency matrices for all iterations after burn-in. It is needed for monitoring the convergence of the BD-MCMC algorithm.
vector which includes the waiting times for all iterations after burn-in. It is needed for monitoring the convergence of the BD-MCMC algorithm.
there are two options: (1) an (\(n \times p\)) matrix or a data.frame corresponding to the data,
(2) an (\(p \times p\)) covariance matrix as \(S=X'X\) which \(X\) is the data matrix
(\(n\) is the sample size and \(p\) is the number of variables).
It also could be an object of class "sim", from function bdgraph.sim.
The input matrix is automatically identified by checking the symmetry.
number of observations. It is needed if the "data" is a covariance matrix.
character with two options "ggm" (default), "dgm" and "dgm-binary".
Option "ggm" is for Gaussian graphical models based on Gaussianity assumption.
Option "dgm" is for discrete graphical models for the count data.
Option "dgm-binary" is for discrete graphical models for the data that are binary.
for only 'count' data which method = "dgm" or method = "dgm-binary".
character with two options "bdmcmc" (default) and "rjmcmc".
Option "bdmcmc" is based on birth-death MCMC algorithm.
Option "rjmcmc" is based on reverible jump MCMC algorithm.
Option "hc" is based on hill-climbing algorithm; this algorithm is only for count data which method = "dgm" or method = "dgm-binary".
number of iteration for the sampling algorithm.
number of burn-in iteration for the sampling algorithm.
for determining the prior distribution of each edge in the graph. There are two options: a single value between \(0\) and \(1\) (e.g. \(0.5\) as a noninformative prior) or an (\(p \times p\)) matrix with elements between \(0\) and \(1\).
corresponds to a starting point of the graph. It could be an (\(p \times p\)) matrix, "empty" (default), or "full".
Option "empty" means the initial graph is an empty graph and "full" means a full graph.
It also could be an object with S3 class "bdgraph" of R package BDgraph or the class "ssgraph" of R package ssgraph::ssgraph();
this option can be used to run the sampling algorithm from the last objects of previous run (see examples).
it is only for the BDMCMC algorithm (algorithm = "bdmcmc").
It is for simultaneously updating multiple links at the same time to update graph in the BDMCMC algorithm.
value of the hyper parameter of Dirichlet, which is a prior distribution.
logical: if FALSE (default), the adjacency matrices are NOT saved. If TRUE, the adjacency matrices after burn-in are saved.
number of cores to use for parallel execution.
The case cores = "all" means all CPU cores to use for parallel execution.
character with two options "or" (default) and "and". It is for hill-climbing algorithm.
logical: if TRUE (default), report/print the MCMC running time.
Reza Mohammadi a.mohammadi@uva.nl, Adrian Dobra, and Johan Pensar
Mohammadi, R., Schoonhoven, M., Vogels, L., and Birbil, S.I. (2023) Large-scale Bayesian Structure Learning for Gaussian Graphical Models using Marginal Pseudo-likelihood, arXiv preprint, tools:::Rd_expr_doi("10.48550/arXiv.2307.00127")
Dobra, A. and Mohammadi, R. (2018). Loglinear Model Selection and Human Mobility, Annals of Applied Statistics, 12(2):815-845, tools:::Rd_expr_doi("10.1214/18-AOAS1164")
Mohammadi, A. and Wit, E. C. (2015). Bayesian Structure Learning in Sparse Gaussian Graphical Models, Bayesian Analysis, 10(1):109-138, tools:::Rd_expr_doi("10.1214/14-BA889")
Vogels, L., Mohammadi, R., Schoonhoven, M., and Birbil, S.I. (2023) Bayesian Structure Learning in Undirected Gaussian Graphical Models: Literature Review with Empirical Comparison, arXiv preprint, tools:::Rd_expr_doi("10.48550/arXiv.2307.02603")
Mohammadi, A. and Dobra, A. (2017). The R Package BDgraph for Bayesian Structure Learning in Graphical Models, ISBA Bulletin, 24(4):11-16
Pensar, J. et al (2017) Marginal pseudo-likelihood learning of discrete Markov network structures, Bayesian Analysis, 12(4):1195-215, tools:::Rd_expr_doi("10.1214/16-BA1032")
Mohammadi, R. and Wit, E. C. (2019). BDgraph: An R Package for Bayesian Structure Learning in Graphical Models, Journal of Statistical Software, 89(3):1-30, tools:::Rd_expr_doi("10.18637/jss.v089.i03")
bdgraph, bdgraph.dw, bdgraph.sim, summary.bdgraph, compare
# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 70, p = 5, size = 7, vis = TRUE )
bdgraph.obj <- bdgraph.mpl( data = data.sim, iter = 500 )
summary( bdgraph.obj )
# To compare the result with true graph
compare( bdgraph.obj, data.sim, main = c( "Target", "BDgraph" ) )
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