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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, May 30, 2000}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Laura Lazzeroni}
\centerline{\sl Stanford University}
\centerline{\sl Art Owen}
\centerline{\sl Stanford University}
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\centerline{\bf Plaid Models}
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This talk describes the plaid model, a tool for exploratory analysis of
multivariate data. The motivating application is the search for
interpretable biological structure in gene expression microarray data.
Interpretable structure can mean that a set of genes has a similar
expression pattern, in the samples under study, or in just a subset of them
(such as the cancerous samples).

A set of genes behaving similarly in a set of samples, defines what we call
a ``layer''.  These are very much like clusters, except that: genes can
belong to more than one layer or to none of them, the layer may be defined
with respect to only a subset of the samples, and the role of genes and
samples is symmetric in our formulation. 

The plaid model is a superposition of two way anova models, each defined
over subsets of genes and samples. We will present the plaid model, an
interior point style algorithm for fitting it, and some examples from yeast
DNA arrays and other problems. 

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