FDR, ODP and Bayesian Decision Rules

Peter Mueller
Department of Biostatistics
M.D. Anderson Cancer Center

Wednesday, November 15th 2006
3:30pm
Moos 2-690
Minneapolis Campus

Abstract:

We discuss Bayesian approaches to multiple comparison problems, using a decision theoretic perspective to critically compare competing approaches. We set up decision problems that lead to the use of FDR-based rules and generalizations. Alternative definitions of the probability model and the utility function lead to different rules and problem-specific adjustments. Using a loss function that controls realized FDR we derive an optimal Bayes rule that is a variation of the
Benjamini and Hochberg(1995) procedure.

We discuss an interpretation of the optimal discovery procedure (ODP, Storey 2006) as an approximate Bayes rule in a nonparametric Bayesian model for multiple comparisons. An improved approximation defines a non-parametric Bayesian version of the ODP statistic (BODP). The definition includes multiple shrinkage in clusters. In a simulation study and a data analysis example we show a (small) improvement in frequentist summaries.

A social tea will be held at 3:00 P.M. in A434 Mayo. All are Welcome.
For more details contact 612-624-4655 or see http://www.biostat.umn.edu/seminar_academic.html