Assume is observed, and that it is desired to estimate 8 under squared-error loss. It is felt that 8 has a K(2,3) prior distribution, but the estimated mean and variance could each be in error by 1...

Assume

is observed, and that it is desired to estimate 8 under squared-error loss. It is felt that 8 has a K(2,3) prior distribution, but the estimated mean and variance could each be in error by 1 unit. Hence the class of plausible priors is

(a) Find the range of posterior means, as 1T ranges over r, when x = 2 is observed.

(b) Find the r -posterior expected loss of the Bayes action with respect to the K(2,3) prior, when x = 2 is observed.

(c) For what e is the Bayes action in (b) e-posterior robust?

(d) Repeat parts (a), (b), and (c) for x= 10. (e) Compare the posterior robustness present for x=2 and x= 10.