R/bayesregressB1S1.R

In BayesSummaryStatLM: MCMC Sampling of Bayesian Linear Models via Summary Statistics

## This method uses flat prior for beta, inverse gamma prior for sigmasq

bayesregressB1S1 <- function(xtx, xtx.inv, xty, yty, numsamp.data,
                             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

# simulate betahat

betahat.mean <- xtx.inv%*%(xty)

# posterior variance of betahat

for (i in 2:Tsamp.out){

betahat[i,] <- rmvn(n=1,
                    mu = betahat.mean,
                    sigma = sigmasqhat[i-1]*xtx.inv)

# 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))

}