Essentials of probability theory for statisticians (Q2808586)

The intention of the authors is to write a book on probability theory suitable for students following programs in biostatistics and statistics. This is an ambitious project. The trouble is that the programs at different universities are so diverse that it is practically not possible to write a single book which serves for all.NEWLINENEWLINEIn fact, this is a good book containing well chosen and important topics from probability theory. The presentation is rigorous, and there is one thing to be mentioned which makes the book special. When introducing a new notion or discussing a specific result, the authors prefer first to `open the eyes' of the reader by showing that there are `traps' in the sense that this or that property/result may fail to be true if we are not careful in checking that all conditions are satisfied. In other cases, a property can be true despite an intuitive suggestion that it is wrong. Hence, on the presentation of the material, there are items which are commonly known as counterexamples or paradoxes. The authors are very successful in combining this kind of specific illustrations with other results usually given with their proofs or indicating a reference.NEWLINENEWLINEWe find in this book all essential notions, concepts, specific results, proofs, illustrations by examples, counterexamples and/or paradoxes. The authors are extremely careful when explaining mathematically any `dangerous' place. This for sure will help the reader to better understand everything which is in the book, including the main ideas for solving the exercises.NEWLINENEWLINEIt is important that the authors pay great attention also to applications. We see interesting and convincing illustrations from applied statistics. Most useful are comparisons in a specific situation of using this or that tool considered before. It is more than instructive for the reader to see why some rule does not work, and what should be required in order the rule to be correctly applicable. To make this clear: a reader will be successful, well motivated and ready to work out details given in the text.NEWLINENEWLINEThe book is addressed to students in applied statistics, however any teacher of a course in probability and statistics, at any level, can also benefit a lot. The book can be considered as a kind of extended handbook which is good for anybody who has something to do with probability and statistics.NEWLINENEWLINEThe material is well chosen and structured. All notions and concepts of modern probability are discussed in the manner chosen by the authors. There is a substantial and rigorous mathematics used. The presentation is smooth.NEWLINENEWLINEIn several cases, the authors use quite an original way to express the essence of this or that. E.g, three of the sections are: ``The meaninglessness of post-facto probability calculations'', ``Expect the unexpected from conditional expectations'', ``An erroneous application of Slutsky's theorem''. The reader should appreciate this fresh style.NEWLINENEWLINEThis reviewer was able to find only a few typos and places needing minor corrections. This information and a suggestions to include a few important references will be sent to the authors.NEWLINENEWLINEOnce again: students, teachers and applied scientists will benefit a lot from this excellent book.NEWLINENEWLINEFinally, congratulations not only to the authors but also to the publisher for arranging (hence paying to) 4 independent reviewers to work on the text before the publication of the book. This is the right way to proceed in order to produce an excellent book.