7.12 Consider a hierarchical Bayes estimator for the Poisson model (7.7.15) with loss

(7.7.16). Using the distribution (5.6.27) for the hyperparameter

b, show that the Bayes estimator is

 px¯ + α − k px¯ + pa + α + β − k



(a + xi − k).

[Hint: Show that the Bayes estimator is E(λ1−k |x)/E(λ−k |x) and that E(λr

|x) =

H(px¯ + pa + α + β)H(px¯ + α + r)

H(px¯ + α)H(px¯ + pa + α + β + r)

H(a + xi + r)

H(a + xi) .