ISBN:
9781402082023
Language:
English
Pages:
Online-Ressource
,
v.: digital
Edition:
Online-Ausg. 2008 Springer eBook Collection. Humanities, Social Science and Law
Series Statement:
Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science 340
Parallel Title:
Erscheint auch als Philosophical Lectures on Probability
Dissertation note:
Lizenzpflichtig
Keywords:
Science Genetic epistemology
;
Distribution (Probability theory)
;
Statistics
;
Social sciences
;
Philosophy (General)
;
Genetic epistemology
;
Mathematics_$xHistory
;
Hochschulschrift
;
Wahrscheinlichkeitstheorie
;
Philosophie
Abstract:
The book contains the transcription of a course on the foundations of probability given by the Italian mathematician Bruno de Finetti in 1979 at the a oeNational Institute of Advanced Mathematicsa in Rome. Bruno de Finetti (1906-1985) is known worldwide as the founder (together with F.P. Ramsey) of the modern personal probability. His fundamental idea of coherence, along with his Dutch Book argument, continues to play a central role in the debates about the foundations of probability and decision theory. Moreover, his notion of exchangeability and the related Representation Theorem are at the
Description / Table of Contents:
CONTENTS; Preface; Editor's Notice; De Finetti's Philosophy of Probability; 1 Introductory Lecture; Against the Axiomatic Approach; Subjectivism; Defining Probability; Proper Scoring Rules; 2 Decisions and Proper Scoring Rules; Why Proper Scoring Rules Are Proper; Probability Depends on the Subject's State of Information; Sequential Decisions; Subjectivism versus Objectivism; For an Omniscient Being Probability Would Not Exist; 3 Geometric Representation of Brier's Rule; Envelope Formed by Straight Lines; Operational Definition of Probability; 4 Bayes' Theorem; Bayes' Theorem and Linearity
Description / Table of Contents:
Statistics and Initial ProbabilitiesBayesian Updating is Not a Corrective Revision; "Adhockeries"; Bayes' Theorem for Random Quantities; Inexpressible Evidence; 5 Physical Probability and Complexity; "Perfect" Dice; The Lottery Paradox; Probability as Frequency; Probability and Physical Laws; Probabilistic Theories as Instruments; Random Sequences; 6 Stochastic Independence and Random Sequences; Logical and Stochastic Independence; Propensities; Independence and Frequentism; Von Mises Collectives; 7 Superstition and Frequentism; The Frequentist Fallacy; Idealized Frameworks
Description / Table of Contents:
The Fallacy of Hypothesis Testing8 Exchangeability; Urn Drawings with Replacement but Without Independence; Induction and "Unknown" Probabilities; Exchangeable Random Quantities; Alleged Objectivity and Convergence of Subjective Probabilities; 9 Distributions; Introductory Concepts; Cumulative Distributions; Continuous Distributions Without Density; The General Case; Characteristic Functions; About Means; 10 The Concept of Mean; Chisini's Serendipity; G -Means and the Nagumo-Kolmogorov Theorem; Statistical Theory of Extremes and Associative Means; Inequalities Among Associative Means
Description / Table of Contents:
Concluding Remarks11 Induction and Sample Randomization; Exchangeability and Convergence to the Observed Frequency; Bayesian Statistics and Sample Randomization; 12 Complete Additivity and Zero Probabilities; The Betting Framework and Its Limits; Finite and Countable Additivity; 'Strict' Coherence; Conditioning on Events of Zero Probability; Allais' Paradox; 13 The Definitions of Probability; Axiomatic, Classical, and Frequentistic Approaches; Indistinguishable Events and Equal Probability; Frequentism and Exchangeability; Von Mises' "Regellosigkeitsaxiom"; 14 The Gambler's Fallacy
Description / Table of Contents:
Against the Measure-Theoretic ApproachGambler's Fallacy and Frequentist Fallacy; Events and Propositions; 15 "Facts" and "Events"; A Pragmatic View of Events; On Elementary Facts; Events and "Phenomena"; 16 "Facts" and "Events": An Example; A Sequence of Coin Tosses; A Graphical Representation; 17 Prevision, Random Quantities, and Trievents; Probability as a Special Case of Prevision; The Conglomerative Property; Trievents; 18 Désiré André's Argument; Heads and Tails: The Gambler's Ruin; The Wiener-Lévy Process; Againon Gambler's Ruin; The Ballot Problem
Description / Table of Contents:
The Power of Désiré André's Argumentative Strategy
Note:
Description based upon print version of record
DOI:
10.1007/978-1-4020-8202-3
URN:
urn:nbn:de:1111-20080724259
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