Source: amazon
Author: Dimitri P. Bertsekas, John N. Tsitsiklis
The authors are Professors in the Department of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology. They are members of the prestigious US National Academy of Engineering. They have written several widely used textbooks and research monographs, both individually and jointly.
Hardcover: 544 pages
Publisher: Athena Scientific; 2nd edition (July 15, 2008)
Language: English
ISBN-10: 188652923X
ISBN-13: 978-1886529236
Product Dimensions: 1.2 x 7.5 x 9.5 inches
Introduction:
An intuitive, yet precise introduction to probability theory, stochastic processes, and probabilistic models used in science, engineering, economics, and related fields. The 2nd edition is a substantial revision of the 1st edition, involving a reorganization of old material and the addition of new material. The length of the book has increased by about 25 percent. The main new feature of the 2nd edition is thorough introduction to Bayesian and classical statistics.
The book is the currently used textbook for "Probabilistic Systems Analysis," an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students. The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject, as well as the fundamental concepts and methods of statistical inference, both Bayesian and classical. It also contains, a number of more advanced topics, from which an instructor can choose to match the goals of a particular course. These topics include transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes.
The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis has been just intuitively explained in the text, but is developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems.
Written by two professors of the Department of Electrical Engineering and Computer Science at the Massachusetts Institute of Technology, and members of the prestigious US National Academy of Engineering, the book has been widely adopted for classroom use in introductory probability courses within the USA and abroad.
From a Review of the 1st Edition:
...it trains the intuition to acquire probabilistic feeling. This book explains every single concept it enunciates. This is its main strength, deep explanation, and not just examples that happen to explain. Bertsekas and Tsitsiklis leave nothing to chance. The probability to misinterpret a concept or not understand it is just... zero. Numerous examples, figures, and end-of-chapter problems strengthen the understanding. Also of invaluable help is the book's web site, where solutions to the problems can be found-as well as much more information pertaining to probability, and also more problem sets. --Vladimir Botchev, Analog Dialogue
Several other reviews can be found in the listing of the first edition of this book. Contents, preface, and more info at publisher's website (Athena Scientific, athenasc com)
Amazon Customer Reviews:
38 of 40 people found the following review helpful
5.0 out of 5 stars Great introduction without unnecessarily mathematical details July 4, 2010
By Vivek Goyal
Format: Hardcover
Overall, this is an outstanding textbook. When one says a book is well written, it could just mean a fluidity sentence-to-sentence or paragraph-to-paragraph. This book has that, but much more importantly, it is organized well. It tells its story in digestible segments that introduce material at a consistent pace and consistent depth throughout. Because of a disciplined avoidance of unnecessary mathematical technicalities and flourishes, the book has a fast pace without being difficult to read. The end result is a solid grounding in the foundations of probability along with introductions to random processes and statistical inference in a remarkably concise volume.
This book is an introduction that requires only basic working knowledge of calculus. This influences the coverage. For example, the authors could easily go further on the topic of Markov chains by requiring just some basic knowledge of linear algebra. Similarly, with linear algebra it would be easy to cover estimation problems involving jointly Gaussian vectors. By keeping the mathematical prerequisites to a minimum, the book is made accessible to a broad audience, early in their education. It is certainly accessible across fields of science and engineering. It could also appeal to any reader who wants to understand some quantification of uncertainty, for example in business or public policy. While the authors are engineering professors, the techniques and examples are not disproportionately targeted to engineering.
This book is not a mathematics book. It does not expose the intricacies of the mathematical foundations of probability, and the typesetting does not include definition, theorem, or proof environments. This is not to say that the book is mathematically inaccurate; at worst, there are some lies of omission. All but the most mathematically-sophisticated readers benefit from this style in a first formal exposure to probability.
This book is also not a philosophical treatise: there is one page on the history of probability and one page on arguments between Bayesians and frequentists. Some probability books seem to be written for an audience that needs to be convinced to learn probability (``See, this result is surprising [or counterintuitive]!''). The present book does not waste its breath like this.
One of the tricks to keeping the book short and the main body text elementary is to include a lot of material in the end-of-chapter problems. The most important such content is provided through problems that have solutions included within the book. Solutions to most of the more routine problems are not included in the book, but they are available for download on the publisher's website. Additional exercises are also available (for anyone, not just instructors) on the publisher's website. Because the authors have squeezed extra material in through the end-of-chapter problems, it may be a fair criticism to say that there aren't very many simple exercises for the reader to work through to learn the material. One way to find material freely online that is aligned with the textbook is to search for "6.041 site:mit.edu".
Some compromises in maintaining a reasonable length for the book show. The final two chapters, covering Bayesian and classical statistical inference, include many new concepts and terms. It is hard to absorb this material without many examples, and the examples in these chapters seem somewhat more difficult than those earlier in the book. Though these chapters comprise almost a quarter of the book, they are still only a brief introduction to statistical inference.
Any fundamental topic is the subject of many textbooks, and which books are best depends on the background and interests of the reader. Having skimmed various other textbooks while teaching a semester-long courses with this one six times, I have come to believe that there is a large audience for which this is the best available textbook. Readers with strong mathematical backgrounds may prefer more mathematical formality, and a thorough introduction to statistical inference requires follow on study, but these facts are not weaknesses of the present book.
Disclaimers: Both authors are my colleagues. While I have read several probability textbooks, this book (in both its editions) is the only one I have used in teaching.