14.9 Consider the following three-level hierarchical model Y y - N O , , var,o‘,>, 0, - “P,, T 2 h of - IG(v,, V Z ) , pt -” “1. CU2L T2 I ~ ( V I t 112h where j e l l , ..., n ) , j e { l ., . . * r , } , and ( r . , ,v2,1.w2,~f , ,q2i)s known.

(a) Derive the closed-form conditional posterior distributions (when possible) required by the Gibbs sampler.

(b) One conditional posterior does not have a closed-form solution. Which one? Describe how variates could be drawn fiom this distribution, thus enabling the Gibbs sampler to be implemented.