bdgraph: Search algorithm in graphical models

Description

As the main function of the BDgraph package, this function consists of several sampling algorithms for Bayesian model determination in undirected graphical models.

Usage

bdgraph( data, n = NULL, method = "ggm", algorithm = "bdmcmc", iter = 5000, 
		  burnin = iter / 2, g.start = "empty", prior.df = 3, 
		  multi.update = NULL, save.all = FALSE )

Arguments

data

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).

The number of observations. It is needed if the "data" is a covariance matrix.

method

A character with two options "ggm" (defult) and "gcgm". Option "ggm" is for Gaussian graphical models based on Gaussianity assumption. Option "gcgm" is for Gaussian copula graphical models for the

algorithm

A character with two options "bdmcmc" (defult) and "rjmcmc". Option "bdmcmc" is based on birth-death MCMC algorithm. Option "rjmcmc" is based on reverible jump MCMC algorithm.

iter

The number of iteration for the sampling algorithm.

burnin

The number of burn-in iteration for the sampling algorithm.

g.start

Corresponds to a starting point of the graph. It could be "empty" (default) and "full". Option "empty" means the initial graph is an empty graph and "full" means a full graph. It also could be an

prior.df

The degree of freedom for G-Wishart distribution, $W_G(b,D)$, which is a prior distribution of the precision matrix. The default is 3.

multi.update

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.

save.all

Logical: if FALSE (default), the adjacency matrices are NOT saved. If TRUE, the adjacency matrices after burn-in are saved.

Value

An object with S3 class "bdgraph" is returned:
p_linksAn upper triangular matrix which corresponds the estimated posterior probabilities of all possible links.
K_hatThe posterior estimation of the precision matrix.
sample_graphsA vector of strings which includes the adjacency matrices of visited graphs after burn-in.
graph_weightsA vector which includes the waiting times of visited graphs after burn-in.
all_graphsA 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.
all_weightsA vector which includes the waiting times for all iterations after burn-in. It is needed for monitoring the convergence of the BD-MCMC algorithm.

References

Mohammadi, A. and E. Wit (2015). Bayesian Structure Learning in Sparse Gaussian Graphical Models, Bayesian Analysis, 10(1):109-138 Mohammadi, A. and E. Wit (2015). BDgraph: An R Package for Bayesian Structure Learning in Graphical Models, arXiv:1501.05108 Mohammadi, A., F. Abegaz Yazew, E. van den Heuvel, and E. Wit (2015). Bayesian Gaussian Copula Graphical Modeling for Dupuytren Disease, arXiv:1501.04849

Examples

Run this code

# Generating multivariate normal data from a 'random' graph
data.sim <- bdgraph.sim( n = 20, p = 6, size = 7, vis = TRUE )
   
bdgraph.obj <- bdgraph( data = data.sim, iter = 1000 )
  
summary( bdgraph.obj )
   
# To compare our result with true graph
compare( data.sim, bdgraph.obj, colnames = c("True graph", "BDgraph") )
   
# Running algorithm with starting points from previous run
bdgraph.obj2 <- bdgraph( data = data.sim, iter = 5000, g.start = bdgraph.obj )
    
compare( data.sim, bdgraph.obj, bdgraph.obj2, 
         colnames = c( "True graph", "Frist run", "Second run" ) )
   
# Generating mixed data from a 'scale-free' graph
data.sim <- bdgraph.sim( n = 50, p = 6, type = "mixed", graph = "scale-free", vis = TRUE )
   
bdgraph.obj <- bdgraph( data = data.sim, method = "gcgm", iter = 10000 )
  
summary( bdgraph.obj )
   
compare( data.sim, bdgraph.obj )

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