Last data update: 2014.03.03

 R: Moment Fractional Bayes Factor Stochastic Search with Global...
FBF_GSR Documentation

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 (davide.altomare@gmail.com).

References

D. Altomare, G. Consonni and L. La Rocca (2013). Objective Bayesian search of Gaussian directed acyclic graphical models for ordered variables with non-local priors. Biometrics.

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

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

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(FBFsearch)
Loading required package: Rcpp
Loading required package: RcppArmadillo
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/FBFsearch/FBF_GS.Rd_%03d_medium.png", width=480, height=480)
> ### Name: FBF_GS
> ### Title: Moment Fractional Bayes Factor Stochastic Search with Global
> ###   Prior for Gaussian DAG Models
> ### Aliases: FBF_GS
> ### Keywords: multivariate models dag stochastic search
> 
> ### ** 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)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

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warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

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warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

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warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

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warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

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warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

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warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

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warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

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warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

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warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

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warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed; change inv(sympd(X)) to inv_sympd(X)

warning: sympd() is deprecated and will be removed;


Created & Maintained by Osamu Ogasawara (osamu.ogasawara@gmail.com) and IMSBIO