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Subjective Probability : The Real Thing - Richard Jeffrey

Subjective Probability

The Real Thing

Paperback Published: 6th September 2004
ISBN: 9780521536684
Number Of Pages: 124

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This book offers a concise survey of basic probability theory from a thoroughly subjective point of view whereby probability is a mode of judgment. Written by one of the greatest figures in the field of probability theory, the book is both a summation and synthesis of a lifetime of wrestling with these problems and issues. After an introduction to basic probability theory, there are chapters on scientific hypothesis-testing, on changing your mind in response to generally uncertain observations, on expectations of the values of random variables, on de Finetti's dissolution of the so-called problem of induction, and on decision theory.

Industry Reviews

'All of this is very lucidly presented and very easy and fun to read. There are a lot of extremely interesting examples and a lot of very instructive and entertaining exercises ... I think it is a terrific introduction to the theme of subjective probability and the Bayesian approach to philosophy of science and epistemology that will be of interest to any professional or scientist as well.' Ellery Eells, University of Wisconsin-Madison 'The book offers a concise survey of basic probability theory from a thoroughly subjective point of view whereby probability theory is a mode of judgement. Written by one of the greatest figures in the field of probability theory, the book is both a summation and a syntheses of a lifetime of wrestling with such problems and issues.' Phinews '... a well written account of basic subjective probability as a tool for decision making under uncertain observations.' Zentralblatt MATH

Prefacep. xi
Probability Primerp. 1
Bets and Probabilitiesp. 1
Why Probabilities Are Additivep. 4
Dutch Book Argument for Finite Additivityp. 5
Dutch Book Argument for Countable Additivityp. 8
Probability Logicp. 9
Conditional Probabilityp. 12
Why "[vertical bar]" Cannot Be a Connectivep. 15
Bayes's Theoremp. 16
Independencep. 17
Objective Chancep. 19
Supplementsp. 22
Testing Scientific Theoriesp. 29
Quantifications of Confirmationp. 30
Observation and Sufficiencyp. 32
Leverrier on Neptunep. 34
Dorling on the Duhem Problemp. 35
Einstein/Newton, 1919p. 37
Bell's Inequalities: Holt/Clauserp. 38
Laplace/Adamsp. 41
Dorling's Conclusionsp. 42
Old News Explainedp. 44
Supplementsp. 48
Probability Dynamics; Collaborationp. 51
Conditioningp. 51
Generalized Conditioningp. 53
Probabilistic Observation Reportsp. 55
Updating Twice: Commutativityp. 57
Updating on Alien Probabilities for Diagnosesp. 58
Updating on Alien Factors for Diagnosesp. 58
Softcore Empiricismp. 59
Expectation Primerp. 62
Probability and Expectationp. 62
Conditional Expectationp. 63
Laws of Expectationp. 65
Median and Meanp. 67
Variancep. 70
A Law of Large Numbersp. 72
Supplementsp. 73
Markov's Inequality: pr(X [greater than or equal] [epsilon]) [less than or equal] ex(X) / [epsilon] if [epsilon] [greater than sign] 0 and X [greater than or equal]p. 73
Chebyshev's Inequality: pr([vertical bar]X - ex(X)[vertical bar] [greater than or equal]) [epsilon]) [less than or equal] var(X) / [epsilon superscript 2] if [epsilon] [greater than sign]p. 73
Many Pairwise Uncorrelated R.V.'sp. 73
Corollary: Bernoulli Trialsp. 74
Noncorrelation and Independencep. 75
Updating on Statisticsp. 76
Where Do Probabilities Come from?p. 76
Probabilities from Statistics: Minimalismp. 76
Probabilities from Statistics: Exchangeabilityp. 78
Exchangeability: Urn Examplesp. 79
Supplementsp. 81
Exchangeability Itselfp. 83
Two Species of Partial Exchangeabilityp. 85
2 x 2 Tablesp. 86
Markov Dependencyp. 86
Finite Forms of de Finetti's Theorem on Partial Exchangeabilityp. 88
Technical Interpolation: Infinite Formsp. 90
Concluding Remarksp. 93
Choosingp. 98
Preference Logicp. 98
Denial Reverses Preferences: A [succeeds] B[vertical, dash] [not sign]B [succeeds] [not sing]Ap. 99
If A [logical and] B [vertical, dash] [perpendicular, bottom] and A [succeeds, equals] B then A [succeeds, equals] A [logical or] B [succeeds, equals] Bp. 100
The "Sure Thing" (or "Dominance") Principle: (A [logical and] B) [succeeds] C,(A [logical and] [not sign]B) [succeeds] C [vertical, dash] A [succeeds] Cp. 100
Bayesian Framesp. 102
Causalityp. 103
Supplements: Newcomb Problemsp. 105
"The Mild and Soothing Weed"p. 106
The Flagship Newcomb Problemp. 109
Hofstadterp. 111
Conclusionp. 112
Referencesp. 115
Indexp. 121
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780521536684
ISBN-10: 0521536685
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 124
Published: 6th September 2004
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.61 x 15.29  x 0.99
Weight (kg): 0.2

Earn 85 Qantas Points
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