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  1. Home
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  3. A Certain Uncertainty
  • Cited by 9
Publisher:
Cambridge University Press
Online publication date:
August 2014
Print publication year:
2014
Online ISBN:
9781139507370
DOI:
https://doi.org/10.1017/CBO9781139507370
Subjects:
Physics and Astronomy, General and Classical Physics, Statistical Physics
Information

Book description

Based around a series of real-life scenarios, this engaging introduction to statistical reasoning will teach you how to apply powerful statistical, qualitative and probabilistic tools in a technical context. From analysis of electricity bills, baseball statistics, and stock market fluctuations, through to profound questions about physics of fermions and bosons, decaying nuclei, and climate change, each chapter introduces relevant physical, statistical and mathematical principles step-by-step in an engaging narrative style, helping to develop practical proficiency in the use of probability and statistical reasoning. With numerous illustrations making it easy to focus on the most important information, this insightful book is perfect for students and researchers of any discipline interested in the interwoven tapestry of probability, statistics, and physics.

Reviews

‘For physicists, it has long been integral to our science to ascribe an uncertainty to every data point, to every inference, to every theory. That is, a measurement is regarded as meaningless without assigning an ‘error bar’ to it. This delightful book by Mark Silverman shows the reader how a physicist does this with the ‘tools of his trade’; namely mathematical analysis, starting with Bayes’ theorem, Poissonian and Gaussian statistics, and progressing through Shannon’s information formulation of entropy. This book is mathematically complete, but not intense, making it intellectually stimulating, with conclusions that are sometimes surprising. I recommend it with considerable enthusiasm.’

Samuel A. Werner - University of Missouri

'A Certain Uncertainty is a 'case study' approach that gives insight in the proper use of statistics through truly interesting physics. This is a book you will read, enjoy, and keep.'

James P. McClymer - University of Maine

'Mark Silverman brings together his wide-ranging expertise to discuss in a unified way the role of probability, statistics, and randomness in all aspects of our understanding of the physical universe. The topics discussed are not only in the basic areas of physics, but also include topics such as air-traffic safety, climate change, and the stock market. As in his previous books, his style is lucid and engaging. A Certain Uncertainty is self-contained with an introductory chapter that includes all of the tools of statistics and probability that are needed for a complete understanding of the material covered in subsequent chapters. Due to its comprehensive and highly informative nature, [this book] is a worthy addition to the bookshelf of any physicist.'

Ronald L. Mallett - University of Connecticut

'… this is a great book. … I particularly like the way statistics and physics are interwoven. The notation is clean and comprehensible … and not obfuscated by a lot of the pretentious notation that has contaminated many more recent books. Although it is not designed as a text, it is definitely going on my recommended reading list.'

David J. Thomson Source: American Journal of Physics

'I really believe that this book would be of interest to a broad public, including students, professors and researchers with a clear interest in randomness, chance, and uncertainty. Furthermore, it provides a very different perspective to statistical physics beyond the standard one …'

Miguel A. F. Sanjuan Source: Contemporary Physics

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Contents

Contents
References

Bibliography

Since A Certain Uncertainty is a narrative of personal scientific investigations, I list in this bibliography only those few books – all from my own library accumulated throughout the years – that I consulted during the course of these researches. It is quite possible that some of the books are long out of print and that others have more recent editions. Nevertheless, my purpose is to comment briefly on books that actually helped me and that I believe are still among the most informative references for physicists and other physical scientists, rather than to provide a long list of titles that I never used. The books commented on below are for the most part mathematically intensive; one will not find long verbal descriptions and colorful figures. Also, be aware that the word “Introduction” in a title does not necessarily mean that the book is elementary.

Probability and statistics

Harold Jeffreys, Theory of Probability 3rd Edition (Oxford, 1961)

  • A classic, compendious treatment of probability in the vanguard of Bayesian methodology.

William Feller, An Introduction to Probability Theory and Its Applications 2nd Edition, Vol. 1 (Wiley, 1950) [Vol. 2 (Wiley, 1966)]

  • An advanced two-volume set (of which I found the first volume to be the more useful), which discusses the application of probability theory, largely from a frequentist perspective, to a variety of problems of physical interest.

Alexander Mood, Franklin Graybill, and Duane Boes, Introduction to the Theory of Statistics 3rd Edition (McGraw-Hill, 1974)

  • An intermediate-level statistics textbook with particularly good discussion of different probability distributions and methods of estimation and hypothesis testing.

[1] Maurice Kendall and Allan Stuart, The Advanced Theory of Statistics, Vol. 1 Distribution Theory, 2nd Edition (Hafner, 1963)
[2] Maurice Kendall and Allan Stuart, The Advanced Theory of Statistics, Vol. 2 Inference and Relationship (Griffin, 1961)
[3] Maurice Kendall, Alan Stuart, and J Keith Ord, The Advanced Theory of Statistics, Vol. 3 Design and Analysis and Time-Series 4th Edition (Macmillan, 1983)

  • This is a definitive advanced treatment of orthodox statistics: a massive three-volume encyclopaedic work that only the most avid statistics enthusiast is likely to want to read cover to cover. It gives the broadest coverage of any statistics reference I know. (My three volumes are of different editions because they were acquired at widely different times from different places.)

George Box, Gwilym Jenkins, and Gregory Reinsel, Time Series Analysis (Pearson, 2005)

  • A classic work, much of it developed by George Box, that presents a thorough treatment of the different classes of model stochastic systems for time-series analysis, forecasting, and control.

Thermodynamics and statistical physics

Herbert Callen, Thermodynamics (Wiley, 1960)

  • This is a graduate-level physics textbook that provides the clearest exposition I have seen of the fundamental principles of equilibrium thermodynamics and the relation between alternative, but equivalent, formulations of these principles by means of Legendre transformations. There is a second edition, which includes more material on statistical thermodynamics, but it is marred (at least my copy is) by printing errors.

E. T. Jaynes, Papers on Probability, Statistics and Statistical Physics, edited by R Rosenkrantz (Kluwer, 1989)

  • This volume includes Jaynes’ eye-opening papers on the principle of maximum entropy as a logical basis for deducing the fundamental relations of equilibrium statistical mechanics, as well as other papers extending the work into the non-equilibrium domain. The papers in their totality provide the most comprehensive and vigorously argued support for a Bayesian approach to probability that I have read.

Information theory

Claude Shannon and Warren Weaver, The Mathematical Theory of Communication (University of Illinois, 1964)

  • This is a clear, concise, introductory account on the relation between entropy, information, and communication by one (Shannon) who helped create the theory and by another (Weaver) noted for his expository ability.

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