Consider the balanced, additive, oneway ANOVA model, EjZ'ICt'glEgj, i=1,...,I,j=1,...,J, (1) where 6,,- \

Consider the balanced, additive, one-way ANOVA model, 1, ... 1 9=1, ... (1) where Eij N (0, a2e), e R, Qi e R, and a2e > 0. We adopt a prior structure that is a product of independent conjugate priors, wherein has a flat prior, Qi N (0, 02), and a2e IG(a, b). Assume that a: , a, and b are known. (a) Derive the full conditional distributions for V, at, , and c2e, necessary for implementing the Gibbs sampler in this problem. [6 pts] (b) What is meant by "convergence diagnosis?" Describe some tools you might use to assist in this regard. What might you do to improve a sampler suffering from "slow conver- gence?" [5 pts] (c) Suppose for simplicity that is also known. What conditions on the data or the priors might lead to slow convergence for and the Qi? (Hint: What conditions weaken the identifiability of the parameters?) [4 pts]