Linked e-resources
Details
Table of Contents
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; 2.3.1 Conditional Probabilities.
2.3.2 Independent Probabilities2.3.3 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; 3.1 Introduction; 3.2 Basic Ideas; 3.2.1 Entropy and Information.
3.2.2 Mutual Information3.2.3 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; 4.2.1 Determination of History Lengths; 4.2.2 Computational Interpretation as Information Transfer.
4.2.3 Conditional Transfer Entropy4.2.4 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; 4.4.4 Granger Causality Versus Transfer Entropy; 4.5 Comparing Transfer Entropy Values; 4.5.1 Statistical Significance.
4.5.2 Normalising Transfer Entropy4.6 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; 6.2 Information Theory Applied to Financial Markets; 6.2.1 Entropy and Economic Diversity: an Early Ecology of Economics; 6.2.2 Maximum Entropy: Maximum Diversity?
2.3.2 Independent Probabilities2.3.3 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; 3.1 Introduction; 3.2 Basic Ideas; 3.2.1 Entropy and Information.
3.2.2 Mutual Information3.2.3 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; 4.2.1 Determination of History Lengths; 4.2.2 Computational Interpretation as Information Transfer.
4.2.3 Conditional Transfer Entropy4.2.4 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; 4.4.4 Granger Causality Versus Transfer Entropy; 4.5 Comparing Transfer Entropy Values; 4.5.1 Statistical Significance.
4.5.2 Normalising Transfer Entropy4.6 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; 6.2 Information Theory Applied to Financial Markets; 6.2.1 Entropy and Economic Diversity: an Early Ecology of Economics; 6.2.2 Maximum Entropy: Maximum Diversity?