Subjective Probability The Real Thing 1st Edition by Richard Jeffrey – Ebook PDF Instant Download/Delivery: 0521829712, 9780521829717
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Product details:
ISBN 10: 0521829712
ISBN 13: 9780521829717
Author: Richard Jeffrey
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.
Table of contents:
1 Probability Primer
1.1 Bets and Probabilities
Odds m:n correspond to probability…
Questions
Discussion
1.2 Why Probabilities Are Additive
1.2.1 Dutch Book Argument for Finite Additivity
1.2.2 Dutch Book Argument for Countable Additivity
1.3 Probability Logic
De Morgan’s Laws
1.4 Conditional Probability
1.5 Why “|” Cannot Be a Connective
1.6 Bayes’s Theorem
1.7 Independence
Definitions
1.8 Objective Chance
1.9 Supplements
2 Testing Scientific Theories
2.1 Quantifications of Confirmation
2.2 Observation and Sufficiency
2.3 Leverrier on Neptune
2.4 Dorling on the Duhem Problem
2.4.1 Einstein/Newton, 1919
2.4.2 Bell’s Inequalities: Holt/Clauser
2.4.3 Laplace/Adams
2.4.4 Dorling’s Conclusions
2.5 Old News Explained
2.6 Supplements
3 Probability Dynamics; Collaboration
3.1 Conditioning
3.2 Generalized Conditioning
3.3 Probabilistic Observation Reports
3.4 Updating Twice: Commutativity
3.4.1 Updating on Alien Probabilities for Diagnoses
3.4.2 Updating on Alien Factors for Diagnoses
3.5 Softcore Empiricism
4 Expectation Primer
4.1 Probability and Expectation
4.2 Conditional Expectation
4.3 Laws of Expectation
4.4 Median and Mean
4.5 Variance
4.6 A Law of Large Numbers
4.7 Supplements
4.7.1 Markov’s Inequality…
4.7.2 Chebyshev’s Inequality…
4.7.3 Many Pairwise Uncorrelated R.V.’s
4.7.4 Corollary: Bernoulli Trials
4.7.5 Noncorrelation and Independence
5 Updating on Statistics
5.1 Where Do Probabilities Come from?
5.1.1 Probabilities from Statistics: Minimalism
5.1.2 Probabilities from Statistics: Exchangeability
5.1.3 Exchangeability: Urn Examples
5.1.4 Supplements
Diaconis and Freedman on de Finetti’s Generalizations of Exchangeability
5.2 Exchangeability Itself
5.3 Two Species of Partial Exchangeability
5.3.1 2 × 2 Tables
5.3.2 Markov Dependency
5.4 Finite Forms of de Finetti’s Theorem on Partial Exchangeability
5.5 Technical Interpolation: Infinite Forms
5.6 Concluding Remarks
Technical Interpolations (2–4)
6 Choosing
6.1 Preference Logic
6.1.1 Denial Reverses Preferences…
6.1.2 If…
6.1.3 The “Sure Thing” (or “Dominance”) Principle…
6.1.3.1 BJ-ing the MM
6.1.3.2 BJ-ing the STP
6.1.4 Bayesian Frames
6.2 Causality
6.3 Supplements: Newcomb Problems
6.3.1 “The Mild and Soothing Weed”
6.3.2 The Flagship Newcomb Problem
6.3.3 Hofstadter
6.3.4 Conclusion
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