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E-raamat: Decision Systems and Nonstochastic Randomness

  • Formaat: PDF+DRM
  • Ilmumisaeg: 17-May-2010
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9781441955487
  • Formaat - PDF+DRM
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  • Formaat: PDF+DRM
  • Ilmumisaeg: 17-May-2010
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9781441955487

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"Decision Systems and Non-stochastic Randomness" presents the first mathematical formalization of the statistical regularities of non-stochastic randomness and demonstrates how these regularities extend the standard probability-based model of decision making under uncertainty, allowing for the description of uncertain mass events that do not fit standard stochastic models. The formalism of statistical regularities developed in this book will have a significant influence on decision theory and information theory as well as numerous other disciplines.

This book presents the first mathematical formalization of the statistical regularities of non-stochastic randomness and demonstrates how these regularities extend the standard probability-based model of decision making under uncertainty, allowing for the description of uncertain mass events that do not fit standard stochastic models.
Preface ix
1 Introduction
1(8)
2 Decision Systems
9(30)
2.1 Preliminaries
9(3)
2.2 The Structure of Decision Systems
12(5)
2.3 Decision Situations
17(8)
2.4 Experiments in Decision Systems
25(2)
2.5 The Decision-Maker
27(3)
2.6 Existence of Uncertainty in Decision Systems
30(3)
2.7 Criterion Choice Rule
33(6)
3 Indifferent Uncertainty
39(32)
3.1 Preliminaries
39(6)
3.2 Γi-independent Sequences
45(7)
3.3 Main Identity
52(4)
3.4 Risk Estimates
56(5)
3.5 Decision-Making under Γi-independence and Antagonistic Games
61(2)
3.6 Some Examples of Γi-Independence
63(8)
4 Nonstochastic Randomness
71(38)
4.1 Preliminaries
71(9)
4.2 The Concept of Statistical Regularity
80(2)
4.3 Sampling Directedness and Statistical Regularity
82(7)
4.4 Coordinated Families of Regularities
89(7)
4.5 Statistical Regularity of a Sequence
96(2)
4.6 Statistical Regularity of Γi-Independence
98(4)
4.7 Sampling Directedness as a Realization of a Random-in-a-Broad-Sense Phenomenon
102(7)
5 General Decision Problems
109(22)
5.1 Preliminaries
109(4)
5.2 On the Preference Relation in Mass Operations
113(10)
5.3 Statistical Regularity and Criterion Choice
123(8)
6 Experiment in Decision Problems
131(18)
6.1 Preliminaries
131(5)
6.2 Informativity of Experiments
136(9)
6.3 Optimality of Experiments
145(4)
7 Informativity of Experiment in Bayesian Decision Problems
149(44)
7.1 Preliminaries
149(7)
7.2 Theorem of Existence and Uniqueness of Uncertainty Functions
156(25)
7.3 The Inverse Theorem
181(3)
7.4 A Generalization to Countable
184(9)
8 Reducibility of Experiments in Multistep Decision Problems
193(12)
8.1 Preliminaries
193(3)
8.2 Reducibility of Bayesian Decision Problems
196(4)
8.3 Reducibility of a General Decision Problem
200(5)
9 Concluding Remarks
205(4)
A Mathematical Supplement
209(56)
A.1 Elements of the Theory of Binary Relations
209(23)
A.2 Elements of the Theory of Real Functions
232(33)
References 265(6)
Index 271