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

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. 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)))

Moment Fractional Bayes Factor Stochastic Search with Local Prior for DAG Models

Description

Estimate the edge inclusion probabilities for a directed acyclic graph (DAG) from observational data, using the moment fractional Bayes factor approach with local prior.

Usage

FBF_LS(Corr, nobs, G_base, h, C, n_tot_mod)

Arguments

Value

An object of class matrix with the estimated edge inclusion probabilities.

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

data(SimDag6) 

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

M_q=FBF_LS(Corr, nobs, matrix(0,q,q), 0, 0.01, 1000)

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

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

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

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

Arguments

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

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))) 

Cell signalling pathway data

Description

Data on a set of flow cytometry experiments on signaling networks of human immune system cells. The dataset includes p=11 proteins and n=7466 samples.

Usage

data(HumanPw)

Format

dataHuman contains the following objects:

Obs

Matrix (7466x11) with the observations.

Perms

List of 5 matrices (1x11) each of which with a permutation of the nodes.

TDag

Matrix (11x11) with the adjacency matrix of the known regulatory network.

Source

Sachs, K., Perez, O., Pe'er, D., Lauffenburger, D., and Nolan, G. (2003). Casual protein- signaling networks derived from multiparameter single-cell data. Science 308, 504-6.

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.

Shojaie, A. and Michailidis, G. (2010). Penalized likelihood methods for estimation of sparse high-dimensional directed acyclic graphs. Biometrika 97, 519-538.

Publishing productivity data

Description

Data on publishing productivity among academics.

Usage

data(PubProd)

Format

dataPub contains the following objects:

Corr

Matrix (7x7) with the correlation matrix of the variables.

nobs

Scalar with the number of observations.

Source

Spirtes, P., Glymour, C., and Scheines, R. (2000). Causation, prediction and search (2nd edition). Cambridge, MA: The MIT Press. pages 1-16.

References

Drton, M. and Perlman, M. D. (2008). A SINful approach to Gaussian graphical model selection. J. Statist. Plann. Inference 138, 1179-1200.

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.

DAG model with 100 nodes and 100 edges

Description

dataSim100 is a list with the adjacency matrix of a randomly generated DAG with 100 nodes and 100 edges, 10 samples generated from the DAG and 5 permutations of the nodes.

Usage

data(SimDag100)

Format

dataSim100 contains the following objects:

Obs

List of 10 matrices (100x100) each of which with 100 observations generated from the DAG.

Perms

List of 5 matrices (1x100) each of which with a permutation of the nodes.

TDag

Matrix (100x100) with the adjacency matrix of the DAG.

Source

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.

References

Shojaie, A. and Michailidis, G. (2010). Penalized likelihood methods for estimation of sparse high-dimensional directed acyclic graphs. Biometrika 97, 519-538.

DAG model with 200 nodes and 100 edges

Description

dataSim200 is a list with the adjacency matrix of a randomly generated DAG with 200 nodes and 100 edges, 10 samples generated from the DAG and 5 permutations of the nodes.

Usage

data(SimDag200)

Format

dataSim200 contains the following objects:

Obs

List of 10 matrices (100x200) each of which with 100 observations simulated from the DAG.

Perms

List of 5 matrices (1x200) each of which with a permutation of the nodes.

TDag

Matrix (200x200) with the adjacency matrix of the DAG.

Source

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.

References

Shojaie, A. and Michailidis, G. (2010). Penalized likelihood methods for estimation of sparse high-dimensional directed acyclic graphs. Biometrika 97, 519-538.

DAG model with 50 nodes and 100 edges

Description

dataSim50 is a list with the adjacency matrix of a randomly generated DAG with 50 nodes and 100 edges, 10 samples generated from the DAG and 5 permutations of the nodes.

Usage

data(SimDag50)

Format

dataSim50 contains the following objects:

Obs

List of 10 matrices (100x50) each of which with 100 observations simulated from the DAG.

Perms

List of 5 matrices (1x50) each of which with a permutation of the nodes.

TDag

Matrix (50x50) with the adjacency matrix of the DAG.

Source

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.

References

Shojaie, A. and Michailidis, G. (2010). Penalized likelihood methods for estimation of sparse high-dimensional directed acyclic graphs. Biometrika 97, 519-538.

DAG model with 6 nodes and 5 edges

Description

dataSim6 is a list with the adjacency matrix of a randomly generated DAG with 6 nodes and 5 edges and 100 correlation matrices generated from the DAG.

Usage

data(SimDag6)

Format

dataSim6 contains the following objects:

Corr

List of 100 matrices (6x6) each of which with a correlation matrix generated from the DAG.

TDag

Matrix (6x6) with the adjacency matrix of the DAG.

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.

Simulated cell signalling pathway data

Description

Data generated from the known regulatory network of human cell signalling data.

Usage

data(SimHumanPw)

Format

dataSimHuman contains the following objects:

Obs

List of 100 matrices (100x11) each of which with 100 observations simulated from the known regulatory network.

Perms

List of 5 matrices (1x11) each of which with a permutation of the nodes.

TDag

Matrix (11x11) with the adjacency matrix of the known regulatory network.

Source

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.

References

Sachs, K., Perez, O., Pe'er, D., Lauffenburger, D., and Nolan, G. (2003). Casual protein- signaling networks derived from multiparameter single-cell data. Science 308, 504-6.

Shojaie, A. and Michailidis, G. (2010). Penalized likelihood methods for estimation of sparse high-dimensional directed acyclic graphs. Biometrika 97, 519-538.