Bayes
2001: Introduction
Bayesian models of perception are becoming increasingly popular. Such models are of use for computer vision, psychophysics, and neuronal modeling. A recent meeting on these topics in Cape Cod (1993) was highly successful and led to a book publication (Perception as Bayesian Inference'' Eds. D.C. Knill and W. Richards. CUP. 1996). Since that time, however, there has been a lot of progress and interest in Bayesian models has greatly increased. Bayes Theorem is commonly ascribed to the Reverent Thomas Bayes (1701-1761) who left one hundred pounds in his will to Richard Price ``now I suppose Preacher at Newington Green.'' Price discovered two unpublished essays among Bayes's papers which he forwarded to the Royal Society. This work made little impact, however, until it was independently discovered a few years later by the great French mathematician Laplace. English mathematicians then quickly rediscovered Bayes' work. Little is known about Bayes and he is considered an enigmatic figure. One leading historian of statistics, Stephen Stigler, has even suggested that Bayes Theorem was really discovered by Nicolas Saunderson, a blind mathematician who was the fourth Lucasian Professor of Mathematics at Cambridge University. (Saunderson was recommended to this chair by Isaac Netwon, the second Lucasian Professor. Recent holders of the chair include the great physicist Paul Dirac and the current holder, Stephen Hawking). Bayes theorem and, in particular, its emphasis on prior probabilities has caused considerable controversy. The great statistician Ronald Fisher was very critical of the ``subjectivist'' aspects of priors. By contrast, a leading proponent I.J. Good argued persuasively that ``the subjectivist (i.e. Bayesian) states his judgements, whereas the objectivist sweeps them under the carpet by calling assumptions knowledge, and he basks in the glorious objectivity of science''. Good, however, also acknowedged that ``there are more forms of Bayesianism than there are actual Bayesians''. More recently, Bayes has emerged from academic controversy and been been applied to a range of practical problems such as detecting missing US Navy submarines and Microsoft's animated paperclip, which offers help to users of its Office software. George Mason's Laskey and others are even planning a London celebration in 2001 to kick off a "century of Bayes". Meanwhile, others are savoring the Reverend's return to respectability. "Twenty-five years ago, we used to sit around and wonder, 'When will our time come?' " says mathematician Persi Diaconis, a Bayesian at Stanford. "Now we can say: 'Our time is now.'
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The Reverent Thomas Bayes (1701-1761) |