It is an excellent textbook on nonparametric series estimators with a number of practical application. Every example is accompanied by comprehensive figures. Software was very helpful.

This is a great book for those working within the field of non-response of surveys.

This book is truly unique in its style and content. It is an encyclopedia on nonuniform and random sampling with many applications. Despite the fact that there are many contributors, the style is tutorial and coherent. It is a must for any library and a reference book for any serious researcher in any related areas. The matlab, C and Mathcad codes attached in the accompanying CD are also very helpful.

This is an excellent textbook for an advanced undergraduate / introductory graduate level course on computational statistics. It is quite accessible to applied statisticians interested in numerical linear algebra, and would be appropriate for an applied statistics course.

In this introductory text space is equally divided into traditional methods (finite difference and spectral) and more modern methods (finite volume and semi-Lagrangian) for solving GFD-related PDEs. The book also contains chapters on filtering of physically insignificant fast waves and on open boundary conditions. Arguably these subjects can be learned by studying a collection of specialty books, but very seldom one finds even-handed treatment of all major techniques in a single book like this. More important, the breadth in scope does not come at the cost of depth or conciseness in presentation. Rather, the book achieves a delightful balance between breadth and depth, as well as between theory and practice. Not only is it an important successer to the long-respected Haltiner and Williams (1984), but it is much more readable.

I used the book to teach a graduate course on numerical methods at the University of Chicago. I could not cover the entire book in a 10-week quarter, but was able to cover chapters 2,3,4 and 5. The clearly written text was very helpful in organizing the class material.

The problems sets at the end of each chapter are also well designed, albeit mostly theoretical. It would be helpful to have separate programming assignments based on these problems, so students can learn how to apply principles into practice.

This book is one of the finest written on the subject and is suitable for readers in a wide variety of fields, including mathematical finance, random dynamical systems, constructive quantum field theory, and mathematical biology. It is certainly well-suited for classroom use, and it includes computer exercises what are definitely helpful for those who need to develop actual computer code to solve the relevant equations of interest. Since it emphasizes the numerical solution of stochastic differential equations, the authors do not give the details behind the theory, but references are given for the interested reader.

As preparation for the study of SDEs, the authors detail some preliminary background on probability, statistics, and stochastic processes in Part 1 of the book. Particularly well-written is the discussion on random number generators and efficient methods for generating random numbers, such as the Box-Muller and Polar Marsaglia methods. Both discrete and continuous Markov processes are discussed, and the authors review the connection between Weiner processes (Brownian motion for the physicist reader) and white noise. The measure-theory foundations of the subject are outlined briefly for the interested reader.

Part 2 begins naturally with an overview of stochastic calculus, with the Ito calculus chosen to show how to generalize ordinary calculus to the stochastic realm. The authors motivate the subject as one in which the functional form of stochastic processes was emphasized, with Ito attempting to find out just when local properties such as the drift and diffusion coefficients can characterize the stochastic process. The Ito formula is shown to be a generalization of the chain rule of ordinary calculus to the case where stochasticity is present. The authors are also careful to distinguish between "random" differential equations and "stochastic" differential equations. The former can be solved by integrating over differentiable sample paths, but in the latter one has to face the nondifferentiability of the sample paths, and hence solutions are more difficult to obtain. The authors give many examples of SDEs that can be solved explicitly, and prove existence and uniqueness theorems for strong solutions of the SDEs. And since ordinary differential equations are usually tackled by Taylor series expansions, it is perhaps not surprising that this technique would be generalized to SDEs, which the authors do in detail in this part. They also outline the differences between the Ito and Stratonovich interpretations of stochastic integrals and SDEs.

Part 3 is definitely of great interest to those who must develop mathematical models using SDEs. The authors carefully outline the reasons where Ito versus the Stratonovich formulations are used, this being largely dependent on the degree of autocorrelation in the processes at hand. The Stratonovich SDE is recommended for cases when the white noise is used as an idealization of a (smooth) real noise process. The authors also show how to approximate Markov chain problems with diffusion processes, which are the solutions of Ito SDEs. Several very interesting examples are given of the applications of stochastic differential equations; the particular ones of direct interest to me were the ones on population dynamics, protein kinetics, and genetics; option pricing, and blood clotting dynamics/cellular energetics.

After a review of discrete time approzimations in ordinary deterministic differential equations, in part 4 the authors show to solve SDEs using this approximation. The familiar Euler approximation is considered, with a simple example having an explicit solution compared with its Euler approximate solution. They also show how to use simulations when an explicit solution is lacking. The importance notions of strong and weak convergence of the approximate solutions are discussed in detail. Strong convergence is basically a convergence in norm (absolute value), while weak convergence is taken with respect to a collection of test functions. Both of these types of convergence reduce to the ordinary deterministic sense of convergence when the random elements are removed.

The discussion of convergence in part 4 leads to a very extensive discussion of strongly convergent approximations in part 5, and weakly convergent approximations in part 6. Stochastic Taylor expansions done with respect to the strong convergence criterion are discussed, beginning with the Euler approximation. More complicated strongly convergent stochastic approximation schemes are also considered, such as the Milstein scheme, which reduces to the Euler scheme when the diffusion coefficients only depend on time. The strong Taylor schemes of all orders are treated in detail. Since Taylor approximations make evaluations of the derivatives necessary, which is computational intensive, the authors discuss strong approximation schemes that do not require this, much like the Runge-Kutta methods in the deterministic case , but the authors are careful to point out that the Runge-Kutta analogy is problematic in the stochastic case. Several of these "derivative-free" schemes are considered by the authors. The authors also consider implicit strong approximation schemes for stiff SDEs, wherein numerical instabilities are problematic. Interesting applications are given for strong approximations for SDEs, such as the Duffing-Van der Pol oscillator, which is very important system in engineering mechanics and phyics, and has been subjected to an incredible amount of research.

More detailed consideration of weak Taylor approximations is given in part 6. The Euler scheme is examined first in the weak approximation, with the higher-order schemes following. Since weak convergence is more stringent than strong convergence, it should come as no surprise that fewer terms are required to obtain convergence, as compared with strong convergence at the same order. This intuition is indeed verified in the discussion, and the authors treat both explicit and implicit weak approximations, along with extrapolation and predictor-corrector methods. And most importantly, the authors give an introduction to the Girsanov methods for variance reduction of weak approximations to Ito diffusions, along with other techniques for doing the same. Those readers involved in constructive quantum field theory will value the treatment on using weak approximations to calculate functional integrals. The approximation of Lyapunov exponents for stochastic dynamical systems is also treated, along with the approximation of invariant measures.

Many years ago the famous statistician Ronald Aylmer Fisher criticized analyses that linked lung cancer to smoking. He argued that these studies had hidden biases because they were not controlled experiments. He proposed that smokers could be different from non-smokers because of a genetic propensity to desire cigarettes and that this genetic trait could be correlated with a higher incidence of lung cancer. Thus it would be possible to see a higher frequency of lung cancer among smokers because of this genetic trait rather than because the smoking itself causes the cancer. As far-fetched as this argument may seem to us today, it is based on sound statistical principles and points out some of the potential problems that occur with observational studies.

Although randomized control trials are the best way to determine differences in treatment effects, they are not always practical or ethical. It would be wrong to randomly choose subjects and force some of them to smoke.

Getting around issues of bias in observational studies was first addressed by Cochran who published a book on the subject in 1983. Rosenbaum came out with his own book in 1995 and this second edition expands and updates that popular text.

In Chapter 1 he present examples of observational studies and raises many important issues. Chapter 2 explains the principles of randomized controlled experiments. In Chapter 3 he covers overt bias and some of the basic methods to adjust for it. The sensitivity of observational studies to hidden biases is covered in Chapter 4.

This book is well written, authoritative and contains numerous references and examples. It also includes a chapter on how to plan an observational study.

Such studies are very important to epidemiologists who want to discover the cause of an epidemic or a disease. With large data base it is possible to remove or adjust biases by matching subjects using propensity scores. Rosenbaum effectively describes how propensity scorng and stratification can be used to make observational studies behave more like randomized control trials.

This is the most exciting book I have ever read in my life! It was so interesting that I could not sleep for two weeks! This book greatly broadened my knowledge on control and filtering. In fact, everything I know on these topics I learned from this book.

Initially, the author provides a nice historical account, presenting the virtues and practical limitations of optimal sequential procedures including Wald's SPRT. He then moves on to provide, in easily understandable terms, reasons why planning to sample in groups can retain many of the nice properties of fully sequential plans without the disadvantages of having to sample one at a time. The rest of the monograph presents the theoretical developments necessary to identify the better plans. The text presents state-of-the-art methods in sequentially planned statistical experiments up until the end of 1992. The references are excellent. However, this is a rapidly developing area in statistics that is seeing a lot of applications in medical trials. Consequently, there have been many advances since the publication of the monograph. The recent book "Group Sequential Methods with Applications to Clinical Trials" by Jennison and Turnbull provides a very recent account (published in 2000) of the group sequential procedures, a subset of the procedures that Schmitz provides for us in this monograph.

This text is a great reference for statistical inference in the presence of ordering or shape restrictions. Isotonic regression, tests for trends and shape restrictions, and many other applied methodologies are presented clearly with illustrative examples. There is a strong theoretical presentation as well, viewing an isotonic regression function simple as a solution to a L2 restricted minimization problem. This blend of theory and application make this an integral text to have at your disposal.