### Use of the Bolstad R library

# Suppose we draw one ball from an urn containing 5 balls, with
# xi = 0,1,2,3,4,5 possible R balls.

library(Bolstad)

help(binodp)

## simplest call with 6 successes observed in 8 trials and a uniform prior

binodp(6,8)

## same as previous example but with more possibilities for pi

binodp(6,8,n.pi=100)

## 6 successes, 8 trials and a non-uniform discrete prior

pi = seq(0,1,by=0.01)
pi.prior = runif(101)
pi.prior = sort(pi.prior/sum(pi.prior))
binodp(6,8,pi,pi.prior)

## 5 successes, 6 trials, non-uniform prior

pi = c(0.3,0.4,0.5)
pi.prior = c(0.2,0.3,0.5)
results = binodp(5,6,pi,pi.prior)

## plot the results from the previous example using a side-by-side barplot

results.matrix = rbind(results$pi.prior,results$posterior)
colnames(results.matrix) = pi
barplot(results.matrix,col=c("red","blue"),beside=TRUE
	,xlab=expression(pi),ylab=expression(Probability(pin)))
box()
legend(1,0.65,legend=c("Prior","Posterior"),fill=c("red","blue"))