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## This method uses normal prior for beta, 1/sigmasq prior for sigmasq
bayesregressB2S2 <- function(xtx,xty,yty,numsamp.data,
beta.prior.mean=rep(0,dim(xtx)[1]),
beta.prior.var=diag(dim(xtx)[1]),
beta.prior.var.inv=chol2inv(chol(beta.prior.var)),
sigmasq.init = 1.0,
Tsamp.out)
{
# define vectors and matrices
ytx<-t(xty)
n <- numsamp.data
Tsamp.out <- Tsamp.out+1
# num.predictors=dim(xtx)[1]
betahat <- matrix(NA,nrow=Tsamp.out,ncol = dim(xtx)[1])
sigmasqhat <- rep(NA,Tsamp.out)
# set starting value for sigmasqhat
sigmasqhat[1] <- sigmasq.init
betahat.pre1 <- beta.prior.var.inv
betahat.pre2 <- betahat.pre1 %*% beta.prior.mean
# posterior variance of betahat
for (i in 2:Tsamp.out){
betahat.var <- chol2inv(chol((betahat.pre1+(1/sigmasqhat[i-1]) * xtx)))
betahat.mean <- betahat.var %*% (betahat.pre2 + (1/sigmasqhat[i-1]) * xty)
betahat[i,] <- rmvn(n=1, mu = betahat.mean,sigma = betahat.var)
# simulate sigmasqhat
sigmasqscale.pre <- (yty - t(betahat[i,]) %*% xty -
ytx %*% betahat[i,] + t(betahat[i,]) %*% xtx %*% betahat[i,])
sigmasqhat[i] <- 1/rgamma(1,shape=n/2,scale=(sigmasqscale.pre/2)^(-1))
} # end i
# remove starting value for sigmasqhat
# and NA for starting value of betahat
betahat <- betahat[-1,]
sigmasqhat <- sigmasqhat[-1]
return(list("beta"=betahat,"sigmasq"=sigmasqhat))
}
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