2.5 Using a histogram prior (pp 27-28).txt

library(LearnBayes)
s=11
f=16

#divide proportion p into ten subintervals

midpt = seq(0.05,0.95, by=0.1)

#assign weights

prior = c(1,5.2,8,7.2,4.6,2.1,0.7,0.1,0,0)

#convert prior weights to probabilities

prior=prior/sum(prior)

#graph of prior

curve(histprior(x,midpt,prior), from=0, to=1, ylab="Prior density", ylim=c(0,.3))

#compute posterior density via "dbeta". Recall that likelihood fcn for a 
#binomial density is beta(s+1,f+1)
#graph of posterior density

curve(histprior(x,midpt,prior)*dbeta(x,s+1,f+1), from=0, to=1, ylab="Posterior density")


#obtain simulated sample
#construct an equally spaced grid of values for p

p=seq(0,1, length=500)

#compute the product of the prior and likelihood ON THIS GRID

post=histprior(p,midpt,prior)*dbeta(p,s+1,f+1)

#convert product on the grid to probabilities

post=post/sum(post)

#take a sample with replacement from the grid using "sample"

ps=sample(p,replace=TRUE, prob=post)

#obtain histogram of simulated values

hist(ps,xlab="p", main="")