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Invited Paper

The International Statistical Institute's 53rd Biennial Session
Seoul, South Korea
August 22-30, 2001

Carey E. Priebe, Daniel Q. Naiman, Jiang Hu

Department of Mathematical Sciences
Whiting School of Engineering
Johns Hopkins University
Baltimore, MD 21218--2682

Title:
  Assessing the Significance of Excursion Regions 
  in Brain Imagery via Importance Sampling

Abstract:
  We consider the problem of assessing the significance of 
excursion regions in brain imagery (PET, fMRI, etc.).
For example, one application of PET involves collecting 
volumetric brain image data from each of a number of subjects 
during two different states, $A$ and $B$, and subtracting these 
to produce a contrast image $C=B-A$. Local regions of high intensity 
in the contrast image $C$ are considered to be regions with 
increased blood flow associated with state $B$ relative to state $A$.  
This in turn is considered to be indicative of increased neural 
activity representing regionally specific effects attributable to 
state $B$.  Assessing the significance of such regions is a stage 
in the attempt to understand the workings of the brain.
  We present a methodology based on importance sampling which provides
a computationally efficient unbiased estimate of the p-value for the 
test of homogeneity (no excursion regions) against the alternative of 
nonhomogeneity (the existence of local excursion regions).  Our 
methodology is indicated in cases where the true p-value is not 
so small as to allow for approximations based on extreme value theory,
yet small enough to prohibit estimation via naive Monte Carlo.

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