23. Refer to Example 2.18. (a) Repeat the analysis of the stack loss data assuming a slightly generalized model where we let j iid

23. Refer to Example 2.18.

(a) Repeat the analysis of the stack loss data assuming a slightly generalized model where we let

πj iid

∼ Bernoulli(θ) , where θ ∼ Unif(0, 1). That is, allow prior variable inclusion probabilities other than 1/2. Do you find any substantial changes to the posteriors for the πj or the μj ?

(b) Repeat your previous solution, but now using dcat and ddirch instead of dbern and dbeta. Is your model more general than that in part (a), in any sense?

(c) Now include prior dependence among the selection probabilities – say, by using a trivariate normal prior on the logit-transformed vector of

πj . Now do your answers change at all?