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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 7, 2000}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 p.m. in 1st Floor Lounge)}

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\centerline{\sl Amir Najmi}
\centerline{\sl Electrical Engineering}
\centerline{\sl Stanford University}
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\centerline{\bf Model Selection, Statistical Inference and Data Compression}
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Abstract: 

The problems of model selection and subsequent estimation of model
parameters are often treated separately. A better-motivated approach might
address these two problem within a single framework. One such framework is
based on the maximum likelihood principle. Pioneered by Herbert Robbins for
the compound estimation problem, the Empirical Bayes approach provides us
with a different framework. This talk derives an Empirical Bayes criterion
for "compound model selection", the selection a single model for multiple
data sets. Under suitable approximations, the model selection criterion can
be specialized to derive a penalty on the maximum log likelihood of any
model. The same approximations also yield reasonable shrinkage estimators.

The particular articulation of the model selection procedure presented in
this talk bears a deep connection to Shannon's theory of lossy data
compression (rate-distortion theory). It can be shown formally that in a
precise statistical sense, the best model is that for which a compression
scheme exists with the smallest distortion plus rate, the distortion
measure being minus the log likelihood of the model density. This result
implies that the theoretical apparatus and algorithms of data compression
may be used to approach problems of statistical inference and model
selection. This work is in keeping with Donoho's "Shannon Estimator"
(presented in a previous Statistics Seminar).

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