# Program 21
# For fixed beta vectors and their prior probabilities, this program uses experimental results to
# calculate the posterior probabilities for those vectors.
# It is necessary to specify (i) the matrix whose columns are the potential parameter vectors,
# (ii) the prior probabilities of these vectors< (iii) values of common parameters, and (iv) the
# results of the experiment

f <- function(xvec)
{
 f <- c(1,xvec)
 f
}

#prior properties of parameters
betamat <- matrix(c(-0.2,-0.2,0.2,0.2,0.8,1.2,0.8,1.2,0.8,1.2,1.2,0.8),4,3)
psivec <- c(0.1,0.2,0.3,0.4)
h <- (dim(betamat))[1]
s <- 4
m <- 2
p <- 3

#properties of design and the experiment
xmat <- matrix(c(-1,-1,0.9689,1,-1,1,1,-1),s,m)
nvec <- c(7,9,5,9)
yvec <- c(2,2,4,4)

probmat <- matrix(0,s,h)
posterior <- rep(0,h)
for (ell in 1:h)
{
 betavec <- betamat[ell,]
 for (em in 1:s)
 {
  xvec <- f(xmat[em,])
  eta <- sum(betavec*xvec)
  probmat[em,ell] = 1/(1+exp(-eta))
 }
}
probmat
condprob <- rep(0,h)
for(i in 1:h)
{condprob[i] <- prod(dbinom(yvec,nvec,probmat[,i]))
}
condprob

temp <- condprob*psivec
posterior <- temp/sum(temp)
posterior