Moment Fractional Bayes Factor Stochastic Search for Regression Models

Description

Estimate the edge inclusion probabilities for a regression model (Y(q) on Y(q-1),...,Y(1)) with q variables from observational data, using the moment fractional Bayes factor approach.

Usage

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

Arguments

Corr

qxq correlation matrix.

nobs

Number of observations.

G_base

Base model.

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 (davide.altomare@gmail.com).

References

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

Examples

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## Not run: 

data(SimDag6) 

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

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


Mt=rev(matrix(Gt[1:(q-1),q],1,(q-1))) #True Model

M_med=M_q
M_med[M_q>=0.5]=1
M_med[M_q<0.5]=0 #median probability model

#Structural Hamming Distance between the true DAG and the median probability DAG
sum(sum(abs(M_med-Mt))) 

## End(Not run)