Figuratively speaking, this is a weighty book (2lbs—465 pages in paperback) that is packed with megabytes of information (no pun intended), from a plethora of sources.
Oxford University Press (OUP) has been generous with font size for which those with faded eye sights will be thankful. Regrettably, OUP’s weight per page seems to be on the rise, because its two other heavy weights, Courant and Robins’ What is Mathematics is 1.75 lbs at 521 pages, and Harold Jeffreys Theory of Probability is 1.5 lbs at 459 pages. This upward trend is anathema to the information age where paper elimination seems to be the call of the day.
The author, Amos Golan, is an acknowledged leader in the field of info-metrics, or better still, one of its originators. In writing this book, he has painfully put together a package that could turn out to be a trigger event in this new and evolving discipline.
Whereas most card—carrying statisticians may not be cognizant as to what info-metrics is, econometricians, engineers, and natural scientists having a statistical orientation, seem to have embraced the subject and appear to be in its driving seat. So, a reader may ask, what is info-metrics?
Chapter 1 of the book attempts to answer this question but looking over it one can’t help but be reminded of the parable of the “Blind Men and the Elephant.” This is because the chapter starts with issues which spawn info-metrics, about the pervasiveness of these issues across all sciences, about how info-metrics attempts to address the issues, and so on, but all of this is said before telling the reader as to what info-metrics means. Later on, when the book does attempt to define info-metrics, several versions are offered. The first version characterizes info-metrics as “a unified constrained optimization framework for information processing, modeling, and inference, for problems across the scientific spectrum.” The second claims that “info-metrics combines the tools and principles of information theory, within a constrained optimization framework, to tackle the universal problems of insufficient information for inference, model, and theory building.” On contemplating this version, one is tempted to ask as to what “insufficient information” means; in the absence of certainty all the information one has can be labeled insufficient. With data at hand, does insufficient information mean its censoring, truncation, or missing values? Moving on to the next defining characterization of info-metrics, it is said that “info-metrics is at the intersection of information theory, statistical methods of inference, applied mathematics, computer science, econometrics, complexity theory, decision analysis, modeling, and the philosophy of science.” Perhaps this last definition best represents the elephant in the room, namely all of the above. But then, like operations research (which can also claim ownership of many of the above), is info-metrics merely an omnibus label for the collection of several disciplines, each having its own tool-kit driven by its own principles? If so, can a collection of disciplines be said constitute a new discipline? If that be the case, what would be the driving principles of this conglomerated discipline? The answer to these questions is best left to the judgment of the reader, but if pushed for an answer the best that seems to evolve in our mind is that info-metrics is a collection of disciplines of the kind mentioned above, plus perhaps others, wherein the Hartley–Shannon–Kolmogorov measure of information is an essential and a driving metric. The author, Amos Golan, may not agree, but if he is sympathetic to this view, it would be a contribution of this review to the loosely defined notion of info-metrics.
Setting aside the matter of definition and interpretation, what can be said about the rest of the book per se? The work is an encyclopedic collection of specifics and details, something which surpasses much that is currently available in the marketplace. The book is rich with describing applications from diverse fields, some traditional, some new, and some novel. This is its strongest card. The author has taken pains to describe in detail the various discipline-based techniques that go to constitute info-metrics, and this is enhanced by providing a rich catalog of references. The book has homework exercises and illustrations, that we find detracting, because its characterizing feature is that of an exhaustive source of reference material.
Should this book be designated for a second edition, or a revision, some kind of reorganization and shuffling can be considered. In the meantime, our recommendation to readers of Technometrics is to acquire a copy of the book, because one never knows when info-metrics, whatever it means, could become mainstream, like data science, and machine learning, and then it will be too late to cry wolf and fill pages of editorials asking as to “who ate our lunch?”
City University of Hong Kong