Question

Problem 3.8(e)

Consider two other priors on $\pi$,

$$p_1(\pi) = 2\pi, \quad (3.35)$$ $$p_0(\pi) = 2 - 2\pi, \quad (3.36)$$

and $0 \le \pi \le 1$. The prior $p_1(\pi)$ favors a r.v. biased to 1, while $p_0$ favors a r.v. biased to 0. Calculate the MAP estimates using these two priors. What is the effective estimate of $\pi$ using these Bayesian estimates? What is the intuitive explanation in terms of "virtual" samples?