Triple-goal estimates in two-stage hierarchical models

Wei Shen, Thomas A. Louis

Research output: Contribution to journalArticlepeer-review

97 Scopus citations


The beauty of the Bayesian approach is its ability to structure complicated models, inferential goals and analyses. To take full advantage of it, methods should be linked to an inferential goal via a loss function. For example, in the two-stage, compound sampling model the posterior means are optimal under squared error loss. However, they can perform poorly in estimating the histogram of the parameters or in ranking them. Triple-goal' estimates are motivated by the desire to have a set of estimates that produce good ranks, a good parameter histogram and good co-ordinate-specific estimates. No set of estimates can simultaneously optimize these three goals and we seek a set that strikes an effective trade-off. We evaluate and compare three candidate approaches: the posterior means, the constrained Bayes estimates of Louis and Ghosh, and a new approach that optimizes estimation of the histogram and the ranks. Mathematical and simulation-based analyses support the superiority of the new approach and document its excellent performance for the three inferential goals.

Original languageEnglish (US)
Pages (from-to)455-471
Number of pages17
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number2
StatePublished - Jan 1 1998
Externally publishedYes


  • Constrained bayes estimates
  • Hierarchical models
  • Histogram estimates
  • Loss functions
  • Ranking

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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