Recent zbMATH articles in MSC 00-01https://www.zbmath.org/atom/cc/00-012021-04-16T16:22:00+00:00WerkzeugThe probability companion for engineering and computer science.https://www.zbmath.org/1456.600012021-04-16T16:22:00+00:00"PrĂ¼gel-Bennett, Adam"https://www.zbmath.org/authors/?q=ai:prugel-bennett.adamFrom the cover of the book: ``This friendly guide is the companion you need to convert pure mathematics into understanding and facility with a host of probabilistic tools. The book provides a high-level view of probability and its most powerful applications. It begins with the basic rules of probability and quickly progresses to some of the most sophisticated modern techniques in use, including Kalman filters, Monte Carlo techniques, machine learning methods, Bayesian inference and stochastic processes. It draws on thirty years of experience in applying probabilistic methods to problems in computational science and engineering, and numerous practical examples illustrate where these techniques are used in the real world. Topics of discussion range from carbon dating to Wasserstein GANs, one of the most recent developments in deep learning. The underlying mathematics is presented in full, but clarity takes priority over complete rigour, making this text a starting reference source for researchers and a readable overview for students.''
The book is very large structured in the Preface, Nomenclature, 12 chapters (divided in 64 subchapters), Appendix A (divided in 12 subchapters), Appendix B (divided in 3 subchapters), Bibliography, Index:
Chapter 1. Introduction -- Chapter 2. Survey of distributions -- Chapter 3. Monte Carlo -- Chapter 4. Discrete random variables -- Chapter 5. The normal distribution -- Chapter 6. Handling experimental data -- Chapter 7. Mathematics of random variables -- Chapter 8. Bayes -- Chapter 9. Entropy -- Chapter 10. Collective behaviour -- Chapter 11. Markov chains -- Chapter 12. Stochastic processes -- Appendix A: Answers to exercises -- Appendix B: Probability distributions.
All the chapters contain examples and finish with exercises, thus we have more than 60 problems for solving. Most of the chapters contain hints for additional reading. The bibliography contains more than 70 references and the index more than 360 items. The short evaluations of the individual references in the bibliography are worth mentioning.
New in the book is the connection to machine learning methods, cp. Subchapter 8.5: Machine learning. The author wrote on page 254: ``There are an enormous number of books on Bayesian approaches to machine learning'', e.g., in the bibliography [\textit{D. Barber}, Bayesian reasoning and machine learning. Cambridge: Cambridge University Press (2012; Zbl 1267.68001); \textit{C. M. Bishop}, Pattern recognition and machine learning. New York, NY: Springer (2006; Zbl 1107.68072); \textit{C. E. Rasmussen} and \textit{C. K. I. Williams}, Gaussian processes for machine learning. Cambridge, MA: MIT Press (2006; Zbl 1177.68165); \textit{J. Pearl}, Probabilistic reasoning in intelligent systems: networks of plausible inference. San Mateo etc.: Morgan Kaufmann Publishers (1989; Zbl 0746.68089); \textit{D. J. C. MacKay}, Information theory, inference and learning algorithms. Cambridge: Cambridge University Press (2003; Zbl 1055.94001)].
The book can be very recommended all readers, who are interested in this field.
Reviewer: Ludwig Paditz (Dresden)