Exact Analysis of Discrete Data
and the observer stays at each of these points for a period of time and records, say, the relative locations of observed singing birds. How should transects and points be laid out in an area? What about edge effects? How can mark–recapture methods be combined with distance methods, say, if birds or whales that can be individually identified are repeatedly observed, or lizards are trapped and released after marking in webs of traps over several nights? Mark–recapture methods are also helpful when two separated observers on a ship each record the tracks of surfacings of observed whales and thus act as controls for each other. These and other issues are discussed in 11 separately authored chapters such as “General Formulation of Distance Sampling,” “Covariate Models for Detection Functions,” “Methods for Incomplete Detection at Distance Zero,” “Design of Distance Sampling Surveys and Geographic Information Systems,” “Adaptive Distance Sampling Surveys,” and “Assessment of Distance Sampling Estimators.” The editors say in the preface that the book is a multiauthored text rather than an edited volume. This helps the reading of individual chapters without having to read all the preceding material. This is good, but also leads to repetition, often of statistically elementary material. Much of distance sampling methodology has recently been developed by the editors of the book and their students. These contributions are for natural reasons given a broader treatment than contributions from other groups. References are given to nearly all the worthwhile publications that I know of (and unfortunately also to quite a number that are less noteworthy), but often only with a few terse words that might not lead the reader to seek out these sources. An area that could have been covered in more depth is, for example, modeling and inference in the rather usual case of overdispersion in the spatial distribution of objects; see, for example, Skaug (2006). I have some misgivings. Likelihood functions and maximum likelihood estimation are treated at various places in the book. The biologist might, however, need more motivation than what is given. The statistician, on the other hand, might find this part of the book somewhat unfocused and elementary. Under the heading “Conventional Distance Sampling: Full Likelihood Examples,” confidence intervals based on assumed chi-squared distribution of the profile deviance are compared to the naïve intervals based on the delta method on the arithmetic and the logarithmic scales. It is the (relative) realized intervals that are compared for various data and models, rather than coverage probabilities and powers for the various confidence interval methods. The authors say that “coverage of the intervals is not known to us.” The models are rather simple, however, and simulation is straightforward. The authors also “speculate that in realistic likelihood models, the profile interval would be generally more sensitive to information in the data than simpler confidence interval methods.” Is this meant as a good or a bad property? Several of the chapters are based on unpublished papers. Perhaps the senior authors should have pushed the juniors a bit harder to get the material properly published before it appeared in a book. Another misgiving is that the subject index is rather scanty. There are many concepts, methods, and terms that are specific to this field of statistics, but are not mentioned in the index. This makes reading an individual chapter harder than necessary. The publisher could also have given page numbers where the various references are mentioned in the text. Despite these critical remarks, the field of distance sampling is important for wildlife management and has been advanced considerably in recent years. Many of these advances are presented in the book, and together with the software developed by the authors, this book and its forerunner will help improve design, field practice, and analysis in the area of distance sampling. Hopefully, the book will also attract statisticians to the field. The book is generally well written and I spotted very few errors or typos. Parts of the book could be used as a text in a joint graduate course or seminar in statistics and ecology. Such a course might lead to Ph.D. projects in either field.