Early in the first week of July, 2000, eighty of us gathered at the University of Leeds for a meeting serving two different purposes. As a conference entitled "Statistics of Directions, Shapes, and Images," it constituted the nineteenth annual (mostly) Leeds Annual Statistics Workshop.
But the workshop was also aimed at celebrating the life and work of our friend Kanti Mardia, who had just stepped down from Chair and Professor of Statistics at Leeds after decades in this dual role. So while many statistics workshops this year must have touched on time-series analysis, few can have begun with a "lifetime-series analysis" such as the scholarly biography of Mardia by Nitis Mukhopadhyay here, and few of the meetings that dealt with circadian rhythms are likely to have included anything resembling Colin Goodall's first overhead transparency. This display, rich in detail even though drawn only over the lunch hour (to incorporate last-minute computations, of course), showed a compelling finding arising from a planned comparison between the "statistician" group (though there may have been some problems with the sampling frame, and maybe missing data) and the "Kanti" group (a sample of one). The analysis was a pair of time series on one common 24-hour axis. The contrast of segmentations it evinced was remarkable. For the Kanti group, rise at 5, work all morning, luncheon walk, work all afternoon, only chocolate to drink; for the comparison group of normals, I forget, but it involved some sort of exponential decline in productivity over the cross-spectrum with caffeination. And hardly any meetings have the geography of antiquarian bookstores as a principal theme.
Now to science. The conference's organizers aimed to span the range of topics on which Kanti has worked over the last twenty years and toward which he has gently directed the interests of so many students and colleagues. Thus nearly every paper at the workshop involved Kanti as instigator or collaborating author. After thirty years during which he was building foundations under spatial, directional, and image statistics, the range of empirical problems to which Kanti's work is relevant in this way is remarkably wide. Beyond morphometrics, papers at the workshop dealt with weather maps, migratory birds, tanks (not always NATO's), face recognition, and emotion recognition. Often we were concerned not only with data acquisition and findings but also with the fundamental problems at the root of estimation in all these domains, including permutation techniques, EM and MCMC methods, and strategies for inference in Kendall shape spaces. The title of the Workshop sorted these themes by data channel (shapes, directions, images), but from the point of view of prosopography it is just as useful to sort them by style. Some of the papers explored statistical problems that began in apercus to which Kanti, in spite of his eighteen-hour workdays, has not yet had time to turn. These seemed to concentrate in the domain of directional data, for which Kanti contributed both the classic book and the latest book (the same book, actually: Statistics of Directional Data, just out in a second edition with Peter Jupp). Among the special topics were problems of score tests (Peter Jupp), change points (Ashis Sengupta), multiscale features (David Foster), permutation distributions (Pranab Sen), and skewed distributions (Toby Lewis and Arthur Pewsey). In the higher-dimensional context of more general aspects of shape, there were presentations on spherical regression (Tom Downs), shape recognition (Shrikant Joshi), and extreme-value theory for Kendall shape coordinates (Ian Dryden).
In other applications, the basic impetus of the Mardia style has already had its impact, placing one application problem after another in the principled framework of likelihood-based inference on equivalence classes ("shape" in the broadest sense), so that progress now is a matter of detailed empirical inspection. This week's examples touched on views of appearance (Tim Cootes), face recognition (Alf Linney) or (a surprisingly distinct task) face verification (Josef Kittler), and special problems of tooth shape from images (D. H. Robinson), motion impairment from 3D surface scans (Z. Mao), glaucomatous optic nerves (Vic Patrangenaru), or images with very difficult problems of impulsive clutter (Azriel Rosenfeld).
Finally, a few papers attempted to challenge the rest of us, perhaps even Kanti himself, with new formal structures similar enough to shape spaces that the matter of their algebraicization could well occupy some of those eighteen-hour days, now freed of administration, pending in his new appointment as Senior Research Professor at Leeds. These extended problems might include statistical frameworks for studying large deformations (Surang Joshi, also S. Zimeras), significance testing in the multiscale context (P. Chaudhuri, also C. A. Murthy), missing data in morphometrics (Fred Bookstein), and the old problem, as yet unformalized, of pattern analysis and inference in images for which the generating model is unsuspected prior to actual data analysis (Julian Besag). The most elegant paper of all was Wilfrid Kendall's, on the notion of "perfect simulation" in MCMC theory, explaining how running simulations from steadily further backward in time can often assure us that they have attained a stationary state at time 0, and so can be used to sample from an MCMC posterior distribution.
As John Kent assured us in his closing remarks, "Shapes, Directions, and Images" are likely to consolidate themselves as one grand theme of 21st century applied statistics. Mardia's work will continue to shape many of the ways the world of statistics construes present knowledge and pending problems to be passed to the new collaborators and new students to come. Our celebration of this single richly contributing career was at the same time a celebration of the past, present, and future of this unexpectedly broad domain of contemporary statistical practice, to which we all intend to go right on contributing.
Fred L. Bookstein
University of Michigan
August 10, 2000
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