Format:
1 Online-Ressource (210 p)
ISBN:
9783319432229
Content:
Preface -- Contents -- List of Key Ideas -- List of Open Research Questions -- List of Key Results -- Symbols -- Acronyms -- List of Tables -- List of Figures -- 1 Introduction -- 1.1 Information Theory -- 1.2 Complex Systems -- 1.2.1 Cellular Automata -- 1.2.2 Spin Models -- 1.2.3 Oscillators -- 1.2.4 Complex Networks -- 1.2.5 Random Boolean Networks -- 1.2.6 Flocking Behaviour -- 1.3 Information Flow and Causality -- 1.4 Applications -- 1.5 Overview -- 2 Statistical Preliminaries -- 2.1 Set Theory -- 2.2 Discrete Probabilities -- 2.3 Conditional, Independent and Joint Probabilities
Content:
2.3.1 Conditional Probabilities -- 2.3.2 Independent Probabilities -- 2.3.3 Joint Probabilities -- 2.3.4 Conditional Independence -- 2.3.5 Time-Series Data and Embedding Dimensions -- 2.3.6 Conditional Independence and Markov Processes -- 2.3.7 Vector Autoregression -- 2.4 Statistical Expectations, Moments and Correlations -- 2.5 Probability Distributions -- 2.5.1 Binomial Distribution -- 2.5.2 Poisson Distribution -- 2.5.3 Continuous Probabilities -- 2.5.4 Gaussian Distribution -- 2.5.5 Multivariate Gaussian Distribution -- 2.6 Symmetry and Symmetry Breaking -- 3 Information Theory
Content:
3.1 Introduction -- 3.2 Basic Ideas -- 3.2.1 Entropy and Information -- 3.2.2 Mutual Information -- 3.2.3 Conditional Mutual Information -- 3.2.4 Kullback-Leibler Divergence -- 3.2.5 Entropy of Continuous Processes -- 3.2.6 Entropy and Kolmogorov Complexity -- 3.2.7 Historical Note: Mutual Information and Communication -- 3.3 Mutual Information and Phase Transitions -- 3.4 Numerical Challenges -- 3.4.1 Calculating Entropy -- 3.4.2 Calculating Mutual Information -- 3.4.3 The Non-stationary Case -- 4 Transfer Entropy -- 4.1 Introduction -- 4.2 Definition of Transfer Entropy
Content:
4.2.1 Determination of History Lengths -- 4.2.2 Computational Interpretation as Information Transfer -- 4.2.3 Conditional Transfer Entropy -- 4.2.4 Source-Target Lag -- 4.2.5 Local Transfer Entropy -- 4.3 Transfer Entropy Estimators -- 4.3.2 Symbolic Transfer Entropy -- 4.3.1 KSG Estimation for Transfer Entropy -- 4.3.3 Open-Source Transfer Entropy Software -- 4.4 Relationship with Wiener-Granger Causality -- 4.4.1 Granger Causality Captures Causality as Predictive of Effect -- 4.4.2 Definition of Granger Causality -- 4.4.3 Maximum-Likelihood Estimation of Granger Causality
Content:
4.4.4 Granger Causality Versus Transfer Entropy -- 4.5 Comparing Transfer Entropy Values -- 4.5.1 Statistical Significance -- 4.5.2 Normalising Transfer Entropy -- 4.6 Information Transfer Density and Phase Transitions -- 4.7 Continuous-Time Processes -- 5 Information Transfer in Canonical Systems -- 5.1 Cellular Automata -- 5.2 Spin Models -- 5.3 Random Boolean Networks -- 5.4 Small-World Networks -- 5.5 Swarming Models -- 5.6 Synchronisation Processes -- 5.7 Summary -- 6 Information Transfer in Financial Markets -- 6.1 Introduction to Financial Markets
Content:
6.2 Information Theory Applied to Financial Markets
Note:
Description based upon print version of record
Additional Edition:
ISBN 9783319432212
Additional Edition:
Print version Bossomaier, Terry R. J. An introduction to transfer entropy Cham : Springer, 2016 ISBN 3319432214
Additional Edition:
ISBN 9783319432212
Language:
English
Keywords:
Informationstheorie
;
Komplexes System
;
Entropie
;
Informationsfluss
;
Electronic books
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