BOOK REVIEW: Probability, Statistical Optics, and Data Testing, 3rd edn

The development of good material for any student course must involve a significant amount of interplay between the recipients and the presenter. There can be no doubt that the third edition of Professor Frieden's book carries the hallmark of such feedback. Not only have some previous discourses been honed but new material has been included, reflecting the ideas and developments in the subject material since the publication of the first edition 20 years ago. The book is unique in the way that it deals with the principles of Probability and Statistics with a slant of application to problems in Optics. The opening chapters are a paragon of clarity in setting the scene for the presentation of the rich material that follows. They contain interesting historical notes presented with gentle humour and the basic definitions associated with experimentation, statistics and probability with the way in which they are interconnected. Although many of the presentations of the statistical/probability concepts generally lead to discussions in the field of optics (e.g. the effects of atmospheric turbulence on the quality of a stellar image) many of the standard statistical tests, such as Chi-square, Student-t etc, are there. Also there are worked out exercises on everyday problems more related to amicable bar discussions on, for example, what is required to decide on whether the flip of a coin has a bias or what is the likelihood of people within a group sharing the same birthday. Much of the material is, however, much deeper than this and, via its underlying theme, links are provided to some of the essentials of very basic physics, including the Heisenberg Uncertainty Principle and the Higgs mass phenomenon. The depth of the coverage is final-year undergraduate to postgraduate level. The philosophy of presentation is that a true understanding of the discipline is best obtained by direct participation through the working out of set problems. The text provides many worked examples with copious and interesting problems (without answers) for engagement. By dipping in, it is also possible to find insight on a particular statistical need that might be to hand and requiring solution. Even with a text of concentrated discourse of some 500 pages, there are omissions. More might have been said perhaps on tests relating measurements to theory or prediction, say those of the Kolmogorov-Smirnov type. The layout is very clear, although the software package behind it has the quirk of sometimes carrying the last section header on the odd-numbered pages to far beyond what is included on those pages. All in all, a rare collection of ideas that stands alone, with unique style, and deserving to be called a true `classic'. David Clarke