Experimental Stochatics (2nd edition)

Abstract

Otto Moeschlin and his co-authors have written a book about simulation of stochastic systems. The book comes with a CD-ROM that contains the experiments discussed in the book, and the text from the book is repeated on the CD-ROM. According to the authors, the aim of the book is to give a quick introduction to stochastic simulation for `all persons interested in experimental stochastics'. To please this diverse audience, the authors offer a book that has four parts. Part 1, called `Artificial Randomness', is the longest of the four parts. It gives an overview of the generation, testing and basic usage of pseudo random numbers in simulation. Although algorithms for generating sequences of random numbers are fundamental to simulation, it is a slightly unusual choice to give it such weight in comparison to other algorithmic topics. The remaining three parts consist of simulation case studies. Part 2, `Stochastic Models', treats four problems---Buffon's needle, a queuing system, and two problems related to the kinetic theory of gases. Part 3 is called `Stochastic Processes' and discusses the simulation of discrete time Markov chains, birth--death processes, Brownian motion and diffusions. The last section of Part 3 is about simulation as a tool to understand the traffic flow in a system controlled by stoplights, an area of research for the authors. Part4 is called `Evaluation of Statistical Procedures'. This section contains examples where simulation is used to test the performance of statistical methods. It covers four examples: the Neymann--Pearson lemma, the Wald sequential test, Bayesian point estimation and Hartigan procedures. The CD-ROM contains an easy-to-install software package that runs under Microsoft Windows. The software contains the text and simulations from the book. What I found most enjoyable about this book is the number of topics covered in the case studies. The highly individual selection of applications, which may serve as a source of inspiration for teachers of computational stochastic methods, is the main contribution of this electronic monograph. However, both the book and software suffer from several severe problems. Firstly, I feel that the structure of the text is weak. Probably this is partly the result of the text from the CD-ROM being put into a book format, but the short paragraphs and poorly structured sentences destroy the reading experience. Secondly, although the software is functional, I believe that, like me, many users will be disappointed by the quality of the user interface and the visualizations. The opportunities to interact with the simulations are limited. Thirdly, the presentation is slightly old fashioned and lacking in pedagogical structure. For example, flow charts and Pascal programs are used to present algorithms. To conclude, I am surprised that this electronic monograph warranted a second edition in this form. Teachers may find the examples useful as a starting point, but students and researchers are advised to look elsewhere.