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Peter Walley
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Statistical Reasoning with Imprecise Probabilities (Chapman & Hall/CRC Monographs on Statistics & Applied Probability) First Edition

by Peter Walley (Author)
4.5 4.5 out of 5 stars 3 ratings
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An examination of topics involved in statistical reasoning with imprecise probabilities. The book discusses assessment and elicitation, extensions, envelopes and decisions, the importance of imprecision, conditional previsions and coherent statistical models.
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  1. ISBN-10
    0412286602
  2. ISBN-13
    978-0412286605
  3. Edition
    First Edition
  4. Publisher
    Chapman and Hall/CRC
  5. Publication date
    December 1, 1990
  6. Language
    English
  7. Dimensions
    6.75 x 1.5 x 9.79 inches
  8. Print length
    720 pages
  9. See all details
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Product details

  • Publisher ‏ : ‎ Chapman and Hall/CRC; First Edition (December 1, 1990)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 720 pages
  • ISBN-10 ‏ : ‎ 0412286602
  • ISBN-13 ‏ : ‎ 978-0412286605
  • Item Weight ‏ : ‎ 2.4 pounds
  • Dimensions ‏ : ‎ 6.75 x 1.5 x 9.79 inches
  • Customer Reviews:
    4.5 4.5 out of 5 stars 3 ratings

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Peter Walley

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Customer reviews

4.5 out of 5 stars
3 global ratings

Top reviews from the United States

Michael Emmett Brady
4.0 out of 5 stars J M Keynes built the foundation for interval estimates
Reviewed in the United States on November 30, 2004
Walley has put together an excellent technical framework for the purpose of analyzing probability statements from the perspective of viewing probability as being essentially interval valued in its most general form.This reviewer agrees with much of what Walley has written.The disagreements would be basically historical in nature and related to Walley's underestimation of how advanced John Maynard Keynes's interval estimate approach to the probability calculus was.Keynes developed a clearcut,technically sophisticated, mathematical framework for interval estimation based on the original work of George Boole in chapters 15 and 17 of his 1921 classic,titled A Treatise on Probability.He applied this framework in his Part III analysis of induction and analogy in chapters 20 and 22 of this book.On pages 135-138,Keynes provided the first systematic treatment of an axiomatic foundation that would apply to both point estimates and interval estimates of probability.Whether Keynes's approach is ultimately judged to be underdeveloped and/or unsatisfactory is besides the point.The fact of the matter is no one even came close to matching Keynes for 40 years.D.Ellsberg's 1961 QJE article and his unpublished 1962 dissertation(published in 2001)represent the only systematic attempt to go to where Keynes had already gone.
5 people found this helpful
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BBVA
5.0 out of 5 stars Sipnosis
Reviewed in the United States on November 9, 2004
Synopsis

This text presents a theory of probabilistic reasoning, statistical inference and decision. The book is concerned with the problems of reasoning under conditions of uncertainty, partial information and ignorance. It is argued that, in order to give appropriate weight to both ignorance and uncertainty, imprecise probabilities need to be assessed. The imprecision can be modelled mathematically by upper and lower probabilities or (more generally) upper and lower previsions. The degree of imprecision can reflect both the amount of information on which probabilities are based and the extent of conflict between different types of information. The book develops mathematical methods for reasoning using imprecise probabilities. These include methods for assessing probabilities, modifying the assessments to achieve coherence, updating them to take account of new information, and combining them to calculate other probabilities, draw conclusions and make decisions. The methods are extended in the second half of the book to construct a general theory of conditional probability and statistical inference. The mathematical theory is based on simple and compelling principles of avoiding sure loss, coherence and natural extension. Careful attention is given to the philosophical foundations, interpretation and justification of the theory. It is compared with alternate theories of inference, including Bayesian theories (which require all probability assesments to be precise), Bayesian sensitivity analysis, the Neyman-Pearson theory of confidence intervals, the Dempster-Shafer theory of belief functions and the theory of fuzzy sets. The theory is applicable to a wide range of disciplines including statistics, decision theory, economics, psychology, philosophy of science, management science, operations research, engineering and artificial intelligence. (References are given to related work in these fields). In fact, the theory has important implications for any field in which the problems of uncertainty and limited information are taken seriously. This book should be of interest to researchers in statistics and those in related disciplines.
3 people found this helpful
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Pieter van Gelder
4.0 out of 5 stars Bayes, fuzzy theory,..., and imprecise probabilities
Reviewed in the United States on October 26, 2000
Couldn't read the whole book (706 pages), but some sections were very interesting. The Laplace example about the probability of the sun not rising was amusing. Since the sun has risen 1 826 213 times the probability of it failing to rise the next day is 1/1826215. Using imprecise probabilities we would have chosen for the lower probabilities. As an applied statistician I would have hoped to see more real case studies. But the theory of imprecise probabilities is still in its "child shoes" and rather philosophical. Case studies might be expected in the coming years...
4 people found this helpful
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