Illustrate the idea of a prior distribution.

beta-binomial.R

n <- 0
k <- 0

a <- c(1, 2, 3, 4, 5)
b <- c(1, 2, 3, 4, 5)
col <- 1:length(a)
names <- c("Carlisle", "B", "C", "D", "E")

plot(NULL, xlim = c(0, 1), ylim = c(0, 3),
     xlab = expression(pi),
     ylab = "Density")
for (i in 1:length(a)) {
  pi <- seq(0, 1, by = 0.01)
  post <- dbeta(pi, a[i] + k, b[i] + n - k)
  lines(pi, post, col = i)
}
legend(legend = names, lty = 1, col = col,
       x = par("usr")[2], xjust = 1,
       y = par("usr")[4], yjust = 1)