The pioneering work of Edwin T. Jaynes in the field of statistical physics, quantum optics, and probability theory has had a significant and lasting effect on the study of many physical problems, ranging from fundamental theoretical questions through to practical applications such as optical image restoration. Physics and Probability is a collection of papers in these areas by some of his many colleagues and former students, based largely on lectures given at a symposium celebrating Jaynes' contributions, on (...) the occasion of his seventieth birthday and retirement as Wayman Crow Professor of Physics at Washington University. The collection contains several authoritative overviews of current research on maximum entropy and quantum optics, where Jaynes' work has been particularly influential, as well as reports on a number of related topics. In the concluding paper, Jaynes looks back over his career, and gives encouragement and sound advice to young scientists. All those engaged in research on any of the topics discussed in these papers will find this a useful and fascinating collection, and a fitting tribute to an outstanding and innovative scientist. (shrink)
An important contribution to the foundations of probability theory, statistics and statistical physics has been made by E. T. Jaynes. The recent publication of his collected works provides an appropriate opportunity to attempt an assessment of this contribution.
Many statistical problems, including some of the most important for physical applications, have long been regarded as underdetermined from the standpoint of a strict frequency definition of probability; yet they may appear wellposed or even overdetermined by the principles of maximum entropy and transformation groups. Furthermore, the distributions found by these methods turn out to have a definite frequency correspondence; the distribution obtained by invariance under a transformation group is by far the most likely to be observed experimentally, in the (...) sense that it requires by far the least “skill.” These properties are illustrated by analyzing the famous Bertrand paradox. On the viewpoint advocated here, Bertrand's problem turns out to be well posed after all, and the unique solution has been verified experimentally. We conclude that probability theory has a wider range of useful applications than would be supposed from the standpoint of the usual frequency definitions. (shrink)
Of course, the rationale of PME is so different from what has been taught in “orthodox” statistics courses for fifty years, that it causes conceptual hangups for many with conventional training. But beginning students have no difficulty with it, for it is just a mathematical model of the natural, common sense way in which anybody does conduct his inferences in problems of everyday life.The difficulties that seem so prominent in the literature today are, therefore, only transient phenomena that will disappear (...) automatically in time. Indeed, this revolution in our attitude toward inference is already an accomplished fact among those concerned with a few specialized applications; with a little familarity in its use its advantages are apparent and it no longer seems strange. It is the idea that inference was once thought to be tied to frequencies in random experiments, that will seem strange to future generations. (shrink)
An important contribution to the foundations of probability theory, statistics and statistical physics has been made by E. T. Jaynes. The recent publication of his collected works provides an appropriate opportunity to attempt an assessment of this contribution. * Review of E. T. JAYNES (1983): Papers on Probability, Statistics and Statistical Physics. Edited by R. D. Rosenkrantz. D. Reidel Publishing Company. US $49.50. Pp. xxiv + 434. We are grateful to Harvey Brown, Kenneth Denbigh, Udi Makov and Oliver (...) Penrose for their valuable criticisms of this paper. (shrink)
E. T. Jaynes' resolution of Bertrand's paradox in terms of invariance principles is criticized. An experimental setup is considered which generates general solutions to Bertrand's problem by rotating a line around a point a distancer+d from a circle of radiusr. The general solution obtained is neither translationally nor scale invariant, but depends on the value ofr/d. Only in the limitr/d » 0, when the line is just translating across the circle, is the distribution translationally invariant and scale invariant. In (...) this limiting case the distribution found is just that obtained by Jaynes. (shrink)