### 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)

n = 1  # draw one ball

x = 1  # one ball drawn and it is a R

# The function binodp with one draw with 6 values of the parameter.

binodp(x,n, uniform = TRUE, n.theta = 6)

# plots of prior and posterior

X11()   # open new graph window

theta = c(0,0.2,0.4,0.6,0.8,1)
theta.prior = c(1/6,1/6,1/6,1/6,1/6,1/6)
results <- binodp(x,n, uniform = FALSE, theta=theta,
                      theta.prior=theta.prior,ret=TRUE)
results.matrix = rbind(results$theta.prior,results$posterior)
colnames(results.matrix) = theta
barplot(results.matrix,col=c("red","blue"),beside=TRUE
         ,xlab=expression(theta),ylab=expression(Probability(theta)))
box()
legend(1,0.25,legend=c("Prior","Posterior"),fill=c("red","blue"))

posterior.mean = sum(theta*results$posterior)
posterior.mean

posterior.sd = sqrt(sum((theta^2)*results$posterior) - posterior.mean^2)
posterior.sd

# Now suppose we draw twice and observer a R and a G.

n = 2

x = 1

X11()   # open new graph window

binodp(x,n, uniform = TRUE, n.theta = 6)

# plots of prior and posterior

X11()   # open new graph window

theta = c(0,0.2,0.4,0.6,0.8,1)
theta.prior = c(1/6,1/6,1/6,1/6,1/6,1/6)
results <- binodp(x,n, uniform = FALSE, theta=theta,
                      theta.prior=theta.prior,ret=TRUE)
results.matrix = rbind(results$theta.prior,results$posterior)
colnames(results.matrix) = theta
barplot(results.matrix,col=c("red","blue"),beside=TRUE
         ,xlab=expression(theta),ylab=expression(Probability(theta)))
box()
legend(1,0.25,legend=c("Prior","Posterior"),fill=c("red","blue"))

posterior.mean = sum(theta*results$posterior)
posterior.mean

posterior.sd = sqrt(sum((theta^2)*results$posterior) - posterior.mean^2)
posterior.sd