## code to accompany the rare event example from lecture 1
## of PSTAT 215A, Bayesian Inference, UCSB
##
## Robert B. Gramacy adapted from Peter Hoff

## plotting the sampling model
barplot(rbind(dbinom(0:20, 20, 0.05),
              dbinom(0:20, 20, 0.1),
              dbinom(0:20, 20, 0.2)),
        names=0:20, beside=TRUE,
        ylab="probability", 
        args.legend=list(x="bottomright", bty="n"),
        legend.text=c("theta=0.05", "theta=0.1", "theta=0.2"))

## plotting the prior
theta <- seq(0,1,length=100)
plot(theta, dbeta(theta, 2, 20), type="l", lwd=2,
     ylab="density", xlab="", bty="n", col="gray")
legend(x="right", bty="n", "prior", lwd=2, col="gray")

## plotting the prior and posterior
theta <- seq(0,1,length=100)
plot(theta, dbeta(theta, 2, 40), type="l", lwd=2,
     ylab="density", xlab="", bty="n")
lines(theta, dbeta(theta, 2, 20), col="gray", lwd=2)
legend(x="right", bty="n", c("posterior", "prior"), lwd=2,
       col=c("black", "gray"))