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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, March 5, 2002}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl David Draper}
\centerline{\sl University of California, Santa Cruz}
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\centerline{\bf Nonparametric prior specification: a case study}

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Investigators working in the Bayesian paradigm have the opportunity/
responsibility to specify prior distributions for unknowns, and to do
sensitivity analyses to see how much a given specification matters. Often,
with a large amount of data and a parametric modeling formulation,
posterior conclusions are stable across plausible variations in how priors
on the parameters are specified, but there are inferential summaries (such
as Bayes factors) for which the answer is sensitive to specification
details even with a fair amount of data. Conventional (e.g., conjugate)
choices are often made when all one really wishes to convey are qualitative
shape characteristics -- such as monotonicity, convexity, or unimodality --
together with quantitative bounds on prior moments or percentiles; in other
words, parametric priors tend to be chosen when what is really desired is
nonparametric prior specification. In this paper we describe a case study
in which bounds on posterior conclusions are derived, via functional
analysis, when the prior is only assumed to be a member of an
infinite-dimensional class of functions. The real-world context of the case
study is detection of a particular kind of possible merchandising swindle.
Our work is related to previous global Bayesian robustness results but
differs from such results in outlook and methods of proof; the latter may
be of interest well beyond the details of this case study.

(This work is joint with John Toland, University of Bath, UK)

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