bdgraph: Graph selection based on birth-death MCMC algorithm

Description

This function is the BD-MCMC algorithm for model selection in undirected Gaussian graphical models based on birth-death MCMC methodology. It works for both low and high dimensional graphs.

Usage

bdgraph(data, n = NULL, npn = "normal", mean = NULL, method = NULL, 
        g.prior = "Uniform", iter = 5000, b = 3, burnin = floor(iter / 2), 
	    thin = 1, lambda = NULL, D = NULL, g.start = "full", K.start = NULL, 
			         mc = 10, trace = TRUE, save.all = FALSE)

Arguments

data

it could be a matrix or a data.frame of the data ( $n \times p$) or it could be a covariance matrix as $S=x'x$ which $x$ is the data matrix.

the number of observations. We need it if the "data" is a covariance matrix.

npn

a character with four options "normal" (default), "shrinkage", "truncation", and "skeptic". Option "normal" means data are coming from multivariate normal distribution. Option "shrinkage" is for the shrunken transformation, option "truncation" is for

mean

If $mean = 0$ means the data have zero mean, otherwise the mean of the data should not be zero.

method

a character with two options "fast" and "mc" to determine a type of BD-MCMC algorithm. Option "fast" is for a high-dimensional graphs (roughly graph with more than 8 nodes which is the default) and option "mc" is based on Monte Carlo approximation for

g.prior

a character for selecting a prior distribution for the graph. It can be either "Uniform" (default) or "Poisson". "Uniform" means discrete uniform distribution for prior distribution of the graph ($G \sim DU(\mathcal{G})$ in which $\mathcal{G}$ is all p

iter

the number of iteration for the BD-MCMC algorithm.

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

burnin

the number of burn-in iteration for the BD-MCMC algorithm.

thin

option for regularly saving part of the iteration. Default is 1 (for saving all iteration).

lambda

a rate for prior distribution of graph when $degree(G) \sim TP(\lambda).$

the positive definite matrix for G-Wishart distribution, $W_G(b,D)$. G-Wishart distribution is the prior distribution of precision matrix.

g.start

it shows the initial graph for the algorithm. It can be either "full" (default), "empty", "glasso", "mb", or "ct". "full" means the initial graph is a full graph and "empty" means a empty graph. "glasso" means the initial graph is a suggested graph by

K.start

it is a starting point for precision matrix. It has to be the positive definite matrix.

the number of iteration for Monte Carlo approximation of normalizing constant in G-Wishart distribution. We need it only when number of nodes in the graph is less than 8.

trace

logical: if TRUE (default), prints out algorithm progress.

save.all

logical: if FALSE (default), we save the adjacency matrices after burn-in. If TRUE, we save all matrices from starting point.

Value

an object with S3 class "bdgraph" as follow:
sample.Ga vector which includes the adjacency matrices for all iteration after burn-in.
weightsa vector which includes the waiting times for all iteration after burn-in.
all.Ga vector which includes the adjacency matrices for all iteration (includes burn-in iteration). We need it for checking the convergency of the BD-MCMC algorithm.
Khatestimation for precision matrix which is a mean of all samples from precision matrices.

References

Mohammadi, A. and E. C. Wit (2012). Gaussian graphical model determination based on birth-death MCMC inference, arXiv:1210.5371v4. http://arxiv.org/abs/1210.5371v4

Examples

Run this code

# generating the data from a random graph
  data.sim <- bdgraph.sim(n = 100, p = 8, size = 10, vis = TRUE)
  
  # Comparing our result with true graph
  output <- bdgraph(data.sim, mean = 0, iter = 2000)
  
  compare(data.sim, output, colnames = c("True graph", "BDgraph"))
  
  output2 <- bdgraph(data.sim, mean = 0, iter = 2000, g.start = output)
  
  compare(data.sim, output, output2, colnames = c("True graph", "Frist run", "Second run"))