FBF_GS {FBFsearch}

Moment Fractional Bayes Factor Stochastic Search with Global Prior for Gaussian DAG Models

Description

Estimate the edge inclusion probabilities for a Gaussian DAG with q nodes from observational data, using the moment fractional Bayes factor approach with global prior.

Usage

FBF_GS(Corr, nobs, G_base, h, C, n_tot_mod, n_hpp)

Arguments

Corr

qxq correlation matrix.

nobs

Number of observations.

G_base

Base DAG.

h

Parameter prior.

C

Costant who keeps the probability of all local moves bounded away from 0 and 1.

n_tot_mod

Maximum number of different models which will be visited by the algorithm, for each equation.

n_hpp

Number of the highest posterior probability models which will be returned by the procedure.

Value

An object of class list with:

M_q

Matrix (qxq) with the estimated edge inclusion probabilities.

M_G

Matrix (n*n_hpp)xq with the n_hpp highest posterior probability models returned by the procedure.

M_P

Vector (n_hpp) with the n_hpp posterior probabilities of the models in M_G.

Author(s)

Davide Altomare ([e-mail]).

References

D. Altomare, G. Consonni and L. La Rocca (2012). Objective Bayesian search of Gaussian directed acyclic graphical models for ordered variables with non-local priors. Article submitted to Biometric Methodology.

Examples

data(SimDag6) 

Corr=dataSim6$SimCorr[[1]]
nobs=50
q=ncol(Corr)
Gt=dataSim6$TDag

Res_search=FBF_GS(Corr, nobs, matrix(0,q,q), 1, 0.01, 1000, 10)
M_q=Res_search$M_q
M_G=Res_search$M_G
M_P=Res_search$M_P

G_med=M_q
G_med[M_q>=0.5]=1
G_med[M_q<0.5]=0 #median probability DAG

G_high=M_G[1:q,1:q] #Highest Posterior Probability DAG (HPP)
pp_high=M_P[1] #Posterior Probability of the HPP

#Structural Hamming Distance between the true DAG and the median probability DAG
sum(sum(abs(G_med-Gt)))
#Structural Hamming Distance between the true DAG and the highest probability DAG 
sum(sum(abs(G_high-Gt)))