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The following examples illustrate the priors implemented so far for linear regression in BGLR. In thes examples we illustrate the use of these priors one at a time.
1. Flat Prior (FIXED)
library(BGLR)
data(mice); X=scale(mice.X[,1:3000]); pheno=mice.pheno
attach(pheno)
fm=BGLR(y=Obesity.BMI,ETA=list( list(~GENDER+CoatColour+CageDensity,model='FIXED')), nIter=6000,burnIn=1000)
fm2=lm(Obesity.BMI~GENDER+CoatColour+CageDensity)
plot(cbind(c(fm$mu,fm$ETA[[1]]$b),coef(fm2))); abline(a=0,b=1)
2. A simple simulation
h2=.5
QTL=floor(seq(from=50,to=ncol(X),length=20))
nQTL=length(QTL); n=nrow(X)
b=rep(1,nQTL)*sqrt(h2/nQTL)
signal=X[,QTL]%*%b
error=rnorm(n,sd=sqrt(1-h2))
y=signal+error
3. Gaussian Prior (BRR, RR-BLUP, BLUP)
nIter=6000; burnIn=1000
fmBRR=BGLR(y=y,ETA=list( list(X=X,model='BRR')),
nIter=nIter,burnIn=burnIn,saveAt='brr_')
plot(abs(fmBRR$ETA[[1]]$b),col=4,cex=.5, type='o',main='BRR');abline(v=QTL,col=2,lty=2)
4. Scaled-t (BayesA)
fmBA=BGLR(y=y,ETA=list( list(X=X,model='BayesA')),
nIter=nIter,burnIn=burnIn,saveAt='ba_')
plot(abs(fmBA$ETA[[1]]$b),col=4,cex=.5, type='o',main='BayesA');abline(v=QTL,col=2,lty=2)
5. Double-Exponential (Bayesian Lasso)
fmBL=BGLR(y=y,ETA=list( list(X=X,model='BL')),
nIter=nIter,burnIn=burnIn,saveAt='bl_')
plot(abs(fmBL$ETA[[1]]$b),col=4,cex=.5, type='o',main='Bayesian Lasso');abline(v=QTL,col=2,lty=2)
6. Point of mass at zero + Gaussian Slab (BayesC)
fmBC=BGLR(y=y,ETA=list( list(X=X,model='BayesC')),
nIter=nIter,burnIn=burnIn,saveAt='bc_')
plot(abs(fmBC$ETA[[1]]$b),col=4,cex=.5, type='o',main='BayesC');abline(v=QTL,col=2,lty=2)
7. Point of mass at zero + t-Slab (BayesB)
fmBB=BGLR(y=y,ETA=list( list(X=X,model='BayesB')),
nIter=nIter,burnIn=burnIn,saveAt='bb_')
plot(abs(fmBB$ETA[[1]]$b),col=4,cex=.5, type='o',main='BayesB');abline(v=QTL,col=2,lty=2)
8. Gaussian prior with set-specific variance (BRR_sets)
tmp=rep(1:ceiling(ncol(X)/5),each=5)[1:ncol(X)]
fmBRR_sets=BGLR(y=y,ETA=list( list(X=X,model='BRR_sets',sets=tmp)),
nIter=nIter,burnIn=burnIn,saveAt='brr_sets_')
plot(abs(fmBRR_sets$ETA[[1]]$b),col=4,cex=.5, type='o',main='BRR_sets');abline(v=QTL,col=2,lty=2)
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