A Tribute to: Keith Worsley — 1951–2009

Abstract

Legend has it that Keith's introduction to neuroimaging followed a chance encounter in a verdant corner of McGill University. One of us (Alan Evans) found Keith gatheringmaple leaves in the fond hope that variations in their shapewould provide a useful source of data, against which to test his statistical ideas. This was in the late 80s when PET scanners had just started producing images of cerebral hemodynamics. It was suggested to Keith that there were more than enough data in functional neuroimaging for his machinations: A suggestion that Keith took seriously. This is one of the key events in the inception of modern imaging neuroscience; although probably not the best day for the study of maple leaves. It is difficult to imagine human brain mapping without Keith's contributions. All mainstream inference in neuroimaging rests upon his ideas and the transcription of those ideas into understandable heuristics and pragmatic computational schemes. Basically, Keith invented a new sort of statistics. Before Keith Worsley, statistical inference in brain mapping was largely limited to discrete or single tests; for example, T-tests on activities in regions of interest. However, continuous image data called for a different sort of inference, based on significant topological features like peaks and excursion sets above some threshold. This should not be confused with spatial statistics of the more traditional sort that predated Keith's contributions, which dealt mostly with kriging and related techniques. Keith introduced a fundamentally different way of characterising interesting features in images that could not be described in terms of simple numbers. The trick was to appeal to differential geometry and topology, which provided a description of the probabilistic behaviour of image data under the null hypothesis in terms of special point processes. This descriptionwas in terms of topological features such as the number of blobs and holes induced by thresholding an image. The result was a very powerful and general framework for topological inference that was grounded in random field theory (Worsley et al., 1992, 1996, 2004). This approach has been at the heart of all mainstream inference in neuroimaging since the early 90s. It is an integral part of all the commonly used voxel-based analysis software and has placed our community at the forefront of statistical developments in this area. Keith's formulation of the problem and its solutions transcend brain imaging and are likely to reach much further in the fullness of time. Random field theory has been used in the analysis of continuous