This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.

Abstract Details

Activity Number: 246
Type: Contributed
Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Consulting
Abstract - #308401
Title: Direct Inference Requiring Only a Touch of Bayes
Author(s): Ralph G. O'Brien*+
Companies: Case Western Reserve University
Address: Dept of Biostatistics and Epidemiology, Cleveland, OH, 44106-4945, USA
Keywords: sequential testing ; meta analysis ; equivalence testing ; non-inferiority testing ; false discovery rate

For some parameter, tau, define a null interval, {0} = {tau0.lo <= tau <= tau0.hi}, with tau0.lo = tau0.hi = tau0 defining a point null value. Non-null regions are {-} = {tau < tau0.lo} and {+} = {tau > tau0.hi}. Let Pr{-}, Pr{0}, Pr{+} be prior probabilities, a "touch of Bayes." Let S be a frequentist statistic for testing hypotheses on tau. A proposed likelihood-based method yields posteriors: Pr[{-}|S], Pr[{+}|S], Pr[{0}|S]; thus providing "direct" inference, as opposed to the "circumstantial" inference obtained using ordinary p-values. This presentation outlines the theory and gives several examples, beginning with a traditional-like, two-sided test of Ho: tau = tau0. Other examples show how the scheme handles tests with an interval null region (e.g., equivalence and non-inferiority tests), and sequential and meta analyses. A related statistical interval for tau is also proposed.

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