summary.post<-function(){
#
# Summaries of Bayesian Posterior Distributions
# 

# Note the following will be assumed alpha=2, beta=2
# X=5, n=10

alpha<-2
beta<-2

xx<-seq(0,1,length=100)

#plot the prior

plot(xx, dbeta(xx,alpha,beta),type="l",lwd=4,lty=2,ylim=c(0,4.5))


x<-5
n<-10
alphastar<-alpha+x
betastar<-beta+(n-x)

#plot the posterior

lines(xx,dbeta(xx,alphastar,betastar),lwd=4,lty=1)

# a different prior -- alpha=10, beta=10

alpha<-10
beta<-10

#plot the new prior

lines(xx,dbeta(xx,alpha,beta),lwd=3,col="red",lty=2)

alphastar<-alpha+x
betastar<-beta+(n-x)

#plot the new posterior

lines(xx,dbeta(xx,alphastar,betastar),lwd=3,col="red",lty=1)

# now summarize!!
alpha<-2
beta<-2
alphastar<-alpha+x
betastar<-beta+(n-x)

postmean<-alphastar/(alphastar+betastar)
postvar<-alphastar*betastar/((alpha+beta+1)*(alphastar+betastar)^2)
poststd<-sqrt(postvar)
postmedian<-qbeta(.5,alphastar,betastar)
postmode<-NULL
return(postmean,postvar,poststd,postmedian,postmode)
}