We have started Ch 3, ¡­

We have started Ch 3, where Sections 3.1-3.4 are curriculum, not 3.5-3.6. I plan to move relatively quickly on to Ch 4, where only Sections 4.1-4.2 are curriculum, and then to Ch 5.

For March 8 we do Exercise 9/2009; Exercise 3.5; Example 3.6 (and try to compute the exact posterior model probabilities, starting from prior model probabilities 0.5 and 0.5 and with uniform priors for (a,b) and (p,q), respectively); and, finally, the following:

Let y1 and y2 be independent from Bin(m1,theta1) and Bin(m2,theta2), and entertain two models: M1 says theta1 = theta2, M2 says otherwise. Take prior probabilities 0.5 and 0.5 and flat uniform priors for the model parameters. Give formulae for Pr(M1 | data) and Pr(M2 | data), and compare with the BIC formulae. Illustrate with (a) y1 = 7 and y2 = 4, with m1 = m2 = 10; and (b) y1 = 58 and y2 = 42, with m1 = m2 = 100.