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1.

電子ブック
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1. Actual causality / ((ebook) :)
Joseph Y. Halpern
出版情報:   1 online resource
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目次情報: 続きを見る
Preface
Introduction and Overview / 1：
Notes
The HP Definition of Causality / 2：
Causal Models / 2.1：
A Formal Definition of Actual Cause / 2.2：
A language for describing causality / 2.2.1：
The HP definition of actual causality / 2.2.2：
Examples / 2.3：
Transitivity / 2.4：
Probability and Causality / 2.5：
Sufficient Causality / 2.6：
Causality in Nonrecursive Models / 2.7：
AC2(bo)vs. AC2(bu) / 2.8：
Causal Paths / 2.9：
Proofs / 2.10：
Proof of Theorem 2.2.3 / 2.10.1：
Proof of Proposition 2.4.6 / 2.10.2：
Proof of Proposition 2.9.2 / 2.10.3：
Graded Causation and Normality / 3：
Defaults, Typicality, and Normality / 3.1：
Extended Causal Models / 3.2：
Graded Causation / 3.3：
More Examples / 3.4：
Knobe effects / 3.4.1：
Bogus prevention / 3.4.2：
Voting examples / 3.4.3：
Causal chains / 3.4.4：
Legal doctrines of intervening causes / 3.4.5：
An Alternative Approach to Incorporating Normality / 3.5：
The Art of Causal Modeling / 4：
Adding Variables to Structure a Causal Scenario / 4.1：
Conservative Extensions / 4.2：
Using the Original HP Definition Instead of the Updated Definition / 4.3：
The Stability of (Non-)Causality / 4.4：
The Range of Variables / 4.5：
Dependence and Independence / 4.6：
Dealing With Normality and Typicality / 4.7：
Proof of Lemma 4.2.2 / 4.8：
Proof of Theorem 4.3.1 / 4.8.2：
Proofs and example for Section 4.4 / 4.8.3：
Complexity and Axiomatization / 5：
Compact Representations of Structural Equations / 5.1：
Compact Representations of the Normality Ordering / 5.2：
Algebraic plausibility measures: the big picture / 5.2.1：
Piggy-backing on the causal model / 5.2.2：
The Complexity of Determining Causality / 5.3：
Axiomatizing Causal Reasoning / 5.4：
Technical Details and Proofs / 5.5：
Algebraic plausibility measures: the details / 5.5.1：
Proof of Theorems 5.3.1(c) and 5.3.2(b) / 5.5.2：
Proof of Theorems 5.4.1, 5.4.2, and 5.4.4 / 5.5.3：
Responsibility and Blame / 6：
A Naive Definition of Responsibility / 6.1：
Blame / 6.2：
Responsibility Normality, and Blame / 6.3：
Explanation / 7：
Explanation: The Basic Definition / 7.1：
Partial Explanations and Explanatory Power / 7.2：
The General Definition of Explanation / 7.3：
Applying the Definitions / 8：
Accountability / 8.1：
Causality in Databases / 8.2：
Program Verification / 8.3：
Last Words / 8.4：
References
Index
Preface
Introduction and Overview / 1：
Notes
2.

電子ブック
ＥＢ
2. High-dimensional probability : : an introduction with applications in data science ((ebook))
Roman Vershynin
出版情報:   1 online resource (xiv, 284 p.)
シリーズ名: Cambridge series in statistical and probabilistic mathematics ; 47
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3.

電子ブック
ＥＢ
3. Bayesian probability theory : : applications in the physical sciences ((ebook))
Wolfgang von der Linden, Graz University of Technology, Institute for Theoretical and Computational Physics, Graz, Austria, Volker Dose, Max Planck Institute for Plasma Physics, Garching, Germany, Udo von Toussaint, Max Planck Institute for Plasma Physics, Garching, Germany
出版情報:   1 online resource (xiii, 637 p.)
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4.

電子ブック
ＥＢ
4. Probability : a very short introduction ((ebook) :)
John Haigh
出版情報: Oxford : Oxford University Press, 2012  1 online resource (128 p.)
シリーズ名: Very short introductions ; 310
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5.

電子ブック
ＥＢ
5. Understanding probability. 3rd ed ((ebook))
Henk Tijms
出版情報:   1 online resource (x, 562 p.)
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目次情報: 続きを見る
Preface
Introduction
Probability in Action / Part I：
Probability questions / 1：
The law of large numbers and simulation / 2：
Probabilities in everyday life / 3：
Rare events and lotteries / 4：
Probability and statistics / 5：
Chance trees and Bayes' rule / 6：
Essentials of Probability / Part II：
Foundations of probability theory / 7：
Conditional probability and Bayes / 8：
Basic rules for discrete random variables / 9：
Continuous random variables / 10：
Jointly distributed random variables / 11：
Multivariate normal distribution / 12：
Conditioning by random variables / 13：
Generating functions / 14：
Discrete-time Markov chains / 15：
Continuous-time Markov chains / 16：
Appendix
Counting methods and ex
Recommended reading
Answers to odd-numbered problems
Bibliography
Index
Preface
Introduction
Probability in Action / Part I：
6.

電子ブック
ＥＢ
6. Probability : theory and examples. 5th ed (: electronic bk)
Rick Durrett
出版情報:   1 online resource (xii, 419 p.)
シリーズ名: Cambridge series in statistical and probabilistic mathematics ; 49
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7.

電子ブック
ＥＢ
7. A course in probability theory. 3rd ed (: electronic bk)
Kai Lai Chung
出版情報: San Diego ; Tokyo : Academic Press, c2001  1 online resource (xvi, 419 p. ; 23 cm)
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目次情報: 続きを見る
Preface to the third edition
Preface to the second edition
Preface to the first edition
Distribution function / 1：
Monotone functions / 1.1：
Distribution functions / 1.2：
Absolutely continuous and singular distributions / 1.3：
Measure theory / 2：
Classes of sets / 2.1：
Probability measures and their distribution functions / 2.2：
Random variable. Expectation. Independence / 3：
General definitions / 3.1：
Properties of mathematical expectation / 3.2：
Independence / 3.3：
Convergence concepts / 4：
Various modes of convergence / 4.1：
Almost sure convergence; Borel-Cantelli lemma / 4.2：
Vague convergence / 4.3：
Continuation / 4.4：
Uniform integrability; convergence of moments / 4.5：
Law of large numbers. Random series / 5：
Simple limit theorems / 5.1：
Weak law of large numbers / 5.2：
Convergence of series / 5.3：
Strong law of large numbers / 5.4：
Applications / 5.5：
Bibliographical Note
Characteristic function / 6：
General properties; convolutions / 6.1：
Uniqueness and inversion / 6.2：
Convergence theorems / 6.3：
Simple applications / 6.4：
Representation theorems / 6.5：
Multidimensional case; Laplace transforms / 6.6：
Central limit theorem and its ramifications / 7：
Liapounov's theorem / 7.1：
Lindeberg-Feller theorem / 7.2：
Ramifications of the central limit theorem / 7.3：
Error estimation / 7.4：
Law of the iterated logarithm / 7.5：
Infinite divisibility / 7.6：
Random walk / 8：
Zero-or-one laws / 8.1：
Basic notions / 8.2：
Recurrence / 8.3：
Fine structure / 8.4：
Conditioning. Markov property. Martingale / 8.5：
Basic properties of conditional expectation / 9.1：
Conditional independence; Markov property / 9.2：
Basic properties of smartingales / 9.3：
Inequalities and convergence / 9.4：
Supplement: Measure and Integral / 9.5：
Construction of measure
Characterization of extensions
Measures in R
Integral
General Bibliography
Index
Preface to the third edition
Preface to the second edition
Preface to the first edition
8.

電子ブック
ＥＢ
8. Probabilistic machine learning : an introduction (: electronic bk)
Kevin P. Murphy
出版情報: [Ann Arbor, Mich.] : ProQuest Ebook Central, [202-]  1 online resource
シリーズ名: Adaptive computation and machine learning
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9.

電子ブック
ＥＢ
9. The Arrow impossibility theorem (: electronic bk)
Eric Maskin, Amartya Sen ; with Kenneth J. Arrow ... [et al.]
出版情報: [S.l.] : EBSCOhost, [20--]  1 online resource (vi, 152 p.)
シリーズ名: Kenneth J. Arrow lecture series ;
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10.

電子ブック
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10. Measure, integral, and probability (: electronic bk)
Marek Capiński and Ekkehard Kopp
出版情報: London : Springer, [20--]  1 online resource (xi, 227 p.)
シリーズ名: Springer undergraduate mathematics series
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目次情報: 続きを見る
Motivation and preliminaries / 1：
Notation and basic set theory / 1.1：
Sets and functions / 1.1.1：
Countable and uncountable sets in <$>\cal {R}<$> / 1.1.2：
Topological properties of sets in <$>\cal {R}<$> / 1.1.3：
The Riemann integral: scope and limitations / 1.2：
Choosing numbers at random / 1.3：
Measure / 2：
Null sets / 2.1：
Outer measure / 2.2：
Lebesgue measurable sets and Lebesgue measure / 2.3：
Basic properties of Lebesgue measure / 2.4：
Borel sets / 2.5：
Probability / 2.6：
Probability space / 2.6.1：
Events: conditioning and independence / 2.6.2：
Proofs of propositions / 2.7：
Measurable functions / 3：
The extended real line / 3.1：
Definition / 3.2：
Examples / 3.3：
Properties / 3.4：
Random variables / 3.5：
Sigma fields generated by random variables / 3.5.2：
Probability distributions / 3.5.3：
Independence of random variables / 3.5.4：
Integral / 3.6：
Definition of the integral / 4.1：
Monotone Convergence Theorems / 4.2：
Integrable functions / 4.3：
The Dominated Convergence Theorem / 4.4：
Relation to the Riemann integral / 4.5：
Approximation of measurable functions / 4.6：
Integration with respect to probability distributions / 4.7：
Absolutely continuous measures: examples of densities / 4.7.2：
Expectation of a random variable / 4.7.3：
Characteristic function / 4.7.4：
Spaces of integrable functions / 4.8：
The space L1 / 5.1：
The Hilbert space L2 / 5.2：
Properties of the L2-norm / 5.2.1：
Inner product spaces / 5.2.2：
Orthogonality / 5.2.3：
The Lp spaces: completeness / 5.3：
Moments / 5.4：
Independence / 5.4.2：
Product measures / 5.5：
Multi-dimensional Lebesgue measure / 6.1：
Product σ-fields / 6.2：
Construction of the product measure / 6.3：
Fubini's Theorem / 6.4：
Joint distributions / 6.5：
Independence again / 6.5.2：
Conditional probability / 6.5.3：
Characteristic functions determine distributions / 6.5.4：
Limit theorems / 6.6：
Modes of convergence / 7.1：
Convergence in probability / 7.2：
Weak law of large numbers / 7.2.2：
Borel-Cantelli lemmas / 7.2.3：
Strong law of large numbers / 7.2.4：
Weak convergence / 7.2.5：
Central Limit Theorem / 7.2.6：
Solutions to exercises / 7.3：
Appendix / 9：
References
Index
Motivation and preliminaries / 1：
Notation and basic set theory / 1.1：
Sets and functions / 1.1.1：
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