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## This method uses normal prior for beta, inverse gamma prior for sigmasq
bayesregressB2S1 <- function(xtx,xty,yty,numsamp.data,
beta.prior.mean = rep(0,dim(xtx)[1]),
beta.prior.var = diag(1.0,dim(xtx)[1]),
beta.prior.var.inv = chol2inv(chol(beta.prior.var)),
inv.gamma.a = 1.0, inv.gamma.b = 1.0,
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){
# use cholesky for matrix inverse
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+inv.gamma.a,scale=(sigmasqscale.pre/2+(1/inv.gamma.b))^(-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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