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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENT SEMINAR}
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\centerline{4:15 p.m., Tuesday, May 21, 2002}
\centerline{Sequoia Hall Room 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Jonathan Taylor}
\centerline{\sl Statistics Department}
\centerline{\sl Stanford University}
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\centerline{\bf A Using the False Discovery Rate for fMRI}
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Functional Magnetic Resonance Imaging, or fMRI, experiments
collect information sequentially about bloodflow throughout the brain
during a psychological experiment. One approach to analyzing such
data, referred to as a ``whole brain analysis'', in contrast to a
``region of interest analysis'' (ROI) which focuses on a small region
of the brain, is to correlate the observed time series at each time
point with an ``ideal'' sequence representing the temporal aspect of
the experimental task.  After this, the 3-dimensional image of
correlations is searched for ``interesting regions'', that is, regions
where the observed signal is highly correlated with the experimental
task.

Due to the huge number of spatial locations, usually of the order of
100-200,000 there is a serious multiple comparison problem to be
addressed in assessing the significance of the observed
correlations. A typical solution is to threshold the image of
correlations at a level chosen to try to control the Family Wise Error
Rate (FWER) at some pre-determined level $\alpha$. Another, more
powerful approach is to use $p$-value dependent thresholds which seek
to control the False Discovery Rate (FDR) at some pre-determined level
$\alpha$.

Both procedures can be thought of as exploratory set estimation
procedures which seek to identify regions that are worthy of further
study, with control of the FWER being more conservative than control
of the FDR.  Both procedures also restrict the regions of interest to
be excursions of the observed image of correlations or the equivalent
$t$-statistics, i.e. if $X_t$ is the image of $t$-statistics, then
both procedures use sets of the form
$$X^{-1}[u,+\infty) = \{t \in \text{brain}: X_t \geq u \}.$$

In this talk, which is a report of work in progress, we review some of
the basic issues described above for the analysis of fMRI data, and
argue that, in some cases, this restriction to the ``excursion sets''
should be relaxed and better results can be obtained, for instance, by
``smoothing'' the binary ``excursion sets''.  One way, though not the
only way, to perform this smoothing is to use some basic tools from
mathematical morphology.  Some simulation results will be presented,
as well as some preliminary analyses of two fMRI examples: one, a
simple ``finger-tapping'' block design experiment and the second, a
more complicated reward anticipation design. 

This is joint work with Brian Knutson in the Psychology department.

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