reject <- function(y,nreps){
#
#
#  This function performs rejection sampling for a posterior as defined
#  in the function "posterior."  The density actually sampled from is
#  that of a random variable 10Y, where Y has the beta(3,3) distribution.
#
#  Warning: This function is not for a general setting!  It is just an
#  example of how to do rejection sampling.
#
#
samples=1:nreps
counts=rep(1,len=nreps)
for(i in 1:nreps){
x=10*rbeta(1,3,3)
ratio=posterior(x,y)/(3*1.7*dbeta(x/10,3,3)/10^7)
check=sign(runif(1)-ratio)
while(check > 0){
counts[i]=counts[i]+1
x=10*rbeta(1,3,3)
ratio=posterior(x,y)/(3*1.7*dbeta(x/10,3,3)/10^7)
check=sign(runif(1)-ratio)
}
samples[i]=x
}
list(counts,samples)
}

posterior = function(theta,y){
n=length(y)
poster=exp(-theta^2/50)
for(i in 1:n){
poster=poster/(1+(y[i]-theta)^2)
}
poster
}