Biostatistics Weekly Seminar

Spatial inference for excursion sets refers to the problem of estimating the set of locations where a function is greater than a threshold. This problem appears in analyses of 2D climate data and 3D brain imaging data. We propose this as an alternative to the standard large-scale multiple testing approach, which does not provide a measure of spatial uncertainty. We directly address the question of where the important effects are by estimating excursion sets and by constructing spatial confidence sets, given as nested regions that spatially bound the true excursion set with a given probability. We develop this approach for excursion sets of the mean function in a signal-plus-noise model, including coefficients in pointwise regression models, and further extend it to the Cohen's d parameter in order to handle spatial heteroscedasticity. Examples and computational issues are discussed for 3D fMRI data.

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2 February 2022
1:30pm