12. Do a simulation comparison of the MLE and three EB approaches: Robbins, the Poisson/gamma, and the Gaussian/Gaussian model for estimating the rate parameter in a Poisson distribution. Note that the Gaussian/Gaussian model is incorrect. Investigate two values of k (10, 20) and several true prior distributions. Study gamma distributions with large and small means and large and small coefficients of variation. Study two distributions that are mixtures of these gammas. Compare approaches relative to SSEL and the maximum coordinate-specific loss and discuss results. You need to design the simulations.

Extra credit: Include in your evaluation a Maritz (forced monotonicity)

improvement of the Robbins rule, and the rule based on the NPML (see Section 7.1 and Subsection 5.3.2 above).