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Subjective Probability

The Real Thing

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Hardcover | 10 June 2004

At a Glance

Hardcover
142 Pages

Dimensions(cm)
22.86 x 15.24 x 1.27

Hardcover

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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

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You Can Find This Book In

Non-Fiction Philosophy Epistemology & The Theory of Knowledge Science Science in General Philosophy of Science Mathematics Probability & Statistics Reference, Information & Interdisciplinary Subjects Research & Information Decision Theory

Preface	p. xi
Probability Primer	p. 1
Bets and Probabilities	p. 1
Why Probabilities Are Additive	p. 4
Dutch Book Argument for Finite Additivity	p. 5
Dutch Book Argument for Countable Additivity	p. 8
Probability Logic	p. 9
Conditional Probability	p. 12
Why "[vertical bar]" Cannot Be a Connective	p. 15
Bayes's Theorem	p. 16
Independence	p. 17
Objective Chance	p. 19
Supplements	p. 22
Testing Scientific Theories	p. 29
Quantifications of Confirmation	p. 30
Observation and Sufficiency	p. 32
Leverrier on Neptune	p. 34
Dorling on the Duhem Problem	p. 35
Einstein/Newton, 1919	p. 37
Bell's Inequalities: Holt/Clauser	p. 38
Laplace/Adams	p. 41
Dorling's Conclusions	p. 42
Old News Explained	p. 44
Supplements	p. 48
Probability Dynamics; Collaboration	p. 51
Conditioning	p. 51
Generalized Conditioning	p. 53
Probabilistic Observation Reports	p. 55
Updating Twice: Commutativity	p. 57
Updating on Alien Probabilities for Diagnoses	p. 58
Updating on Alien Factors for Diagnoses	p. 58
Softcore Empiricism	p. 59
Expectation Primer	p. 62
Probability and Expectation	p. 62
Conditional Expectation	p. 63
Laws of Expectation	p. 65
Median and Mean	p. 67
Variance	p. 70
A Law of Large Numbers	p. 72
Supplements	p. 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.'s	p. 73
Corollary: Bernoulli Trials	p. 74
Noncorrelation and Independence	p. 75
Updating on Statistics	p. 76
Where Do Probabilities Come from?	p. 76
Probabilities from Statistics: Minimalism	p. 76
Probabilities from Statistics: Exchangeability	p. 78
Exchangeability: Urn Examples	p. 79
Supplements	p. 81
Exchangeability Itself	p. 83
Two Species of Partial Exchangeability	p. 85
2 x 2 Tables	p. 86
Markov Dependency	p. 86
Finite Forms of de Finetti's Theorem on Partial Exchangeability	p. 88
Technical Interpolation: Infinite Forms	p. 90
Concluding Remarks	p. 93
Choosing	p. 98
Preference Logic	p. 98
Denial Reverses Preferences: A [succeeds] B[vertical, dash] [not sign]B [succeeds] [not sing]A	p. 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] B	p. 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] C	p. 100
Bayesian Frames	p. 102
Causality	p. 103
Supplements: Newcomb Problems	p. 105
"The Mild and Soothing Weed"	p. 106
The Flagship Newcomb Problem	p. 109
Hofstadter	p. 111
Conclusion	p. 112
References	p. 115
Index	p. 121
Table of Contents provided by Ingram. All Rights Reserved.

Subjective Probability

The Real Thing

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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