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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, June 3, 2003}
\centerline{Sequoia Hall Room 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl David Siegmund}
\centerline{\sl Stanford University}
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\centerline{\bf Gene Mapping and Model Selection}
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Abstract:
The goal of gene mapping is to identify genes associated with
specific traits, e.g., human diseases, quantitative traits in
animal models of human diseases, quantitative traits in agriculturally
important species, etc.  An initial step often involves testing of
markers throughout a genome for linkage to genes contributing to the
trait.
This involves selection of a model for the trait as a 
function of genotype and environment.  The model may involve multiple,
possibly 
interacting genes.  

To map quantitative traits in experimental genetics, Broman and Speed 
(2002, JRSSB) have suggested use of the Bayes Information Criterion
(BIC) 
for model selection.  An issue they must face is that the conditions
imposed
by Schwarz (1968, Ann.  Math. Statist.) to justify the BIC are not met
in 
gene mapping problems, so the BIC penalty of $(k/2) \log n$ for choosing
a model 
with $k$ parameters (when the sample size is $n$) may not be
appropriate.  
In this talk I will re-interpret the BIC argument in terms of p-values
and the 
logic of Bahadur efficiency.  I will then show by  hypothetical
numerical examples 
and examples from the literature how this interpretation would function
in 
selecting models for gene mapping.

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