TRIPLE-GOAL ESTIMATES IN 2-STAGE HIERARCHICAL-MODELS

The beauty of the Bayesian approach is its ability to structure compli cated models, inferential goals and analyses. To take full advantage o f it, methods should be linked to an inferential goal via a loss funct ion. For example, in the two-stage, compound sampling model the poster ior means are optimal under squared error loss. However, they can perf orm poorly in estimating the histogram of the parameters or in ranking them. 'Triple-goal' estimates are motivated by the desire to have a s et of estimates that produce good ranks, a good parameter histogram an d good co-ordinate-specific estimates. No set of estimates can simulta neously optimize these three goals and we seek a set that strikes an e ffective trade-off. We evaluate and compare three candidate approaches : the posterior means, the constrained Bayes estimates of Louis and Gh osh, and a new approach that optimizes estimation of the histogram and the ranks. Mathematical and simulation-based analyses support the sup eriority of the new approach and document its excellent performance fo r the three inferential goals.