Tumor count comparisons: Reconsider the tumor count data in Exercise

3.3:

a) For the prior distribution given in part a) of that exercise, obtain

Pr(B < A|yA, yB) via Monte Carlo sampling.

b) For a range of values of n0, obtain Pr(B < A|yA, yB) for A

gamma(120, 10) and B gamma(12n0, n0). Describe how sensitive

the conclusions about the event {B < A} are to the prior distribution

on B.

c) Repeat parts a) and b), replacing the event {B < A} with the event

{ YB < YA}, where YA and YB are samples from the posterior predictive

distribution.