The Information Theory of Comparisons: With Applications to Statistics and the Social Sciences

Preface
Contents
Intro
1 Partition Entropy
	1.1 Introduction
	1.2 Information, Complexity and Entropy
		1.2.1 Entropic Decompositions
	1.3 Partition Entropy
		1.3.1 Complexity and the Psychology of Investment Decisions
		1.3.2 An Extension: The Frequency Domain
	1.4 Partition Entropy and the Log Odds Function
	1.5 Discrete Valued Random Variables and Histograms
	1.6 Resolving Grade Uncertainty
	1.7 Tail Complexity and Market Clearing Prices
	1.8 Literature Notes
	References
2 Entropic Shifting Perspectives & Applications
	2.1 Introduction
	2.2 Left and Right Entropic Shifts
	2.3 Shift Kernels: Concentrators and Spreaders
		2.3.1 Some Extensions
	2.4 Perspectives on Mixture Distributions
	2.5 The Entropic Kernel: Data Smoothing and End Correction
		2.5.1 End Correction with Kernel Compression
	2.6 The Social Dynamics of Opinion
		2.6.1 The Momentum of Opinion
	2.7 Application of Mixture Theory to Value at Risk
	2.8 Literature Notes
	References
3 Moments, Measures & Metrics
	3.1 Introduction
	3.2 Moments for the Entropic Shifts
	3.3 The Double Smoothing Property
	3.4 Asymmetry and Spread Functions
	3.5 Summary Metrics for Asymmetry and Spread
	3.6 Gini’s Mean Absolute Difference and Welfare Variants
	3.7 The Economic Dynamics of Remuneration Relativities
	3.8 Relationship with Stochastic Dominance
	3.9 Literature Notes
	References
4 Information Comparisons in Practice
	4.1 Introduction
	4.2 Income Distribution
	4.3 Implementation as Entropic Asymmetry and Spread Metrics
		4.3.1 Social Welfare Aspects
		4.3.2 Dynamics: The v-d Phase Plane
	4.4 Application to Stock Market Performance
	4.5 Actuarial Life Expectancy
	4.6 Literature Notes
	References
5 Binary Perspectives for Spread & Asymmetry
	5.1 Introduction
	5.2 A First Approach Based on Spanning
	5.3 Bipolarity: The Entropic Centre and Equivalent Width
	5.4 Polar Asymmetry and Spread Metrics
	5.5 Fund Performance Measures
	5.6 Actuarial Uncertainty Revisited
	5.7 Literature Notes
	References
6 Higher Dimensions
	6.1 Introduction
	6.2 Higher Dimensions: Directional Shifting Perspectives
		6.2.1 Left and Right Hand Smoothing Moments
		6.2.2 Co-smoothing
	6.3 Index Combinations
	6.4 Co-smoothing and the Ordered Mean Difference
		6.4.1 The OMD in Context: Some Financial Decision Theory
		6.4.2 Do Hedge Funds Really Add Value?
	6.5 Literature Notes
	References
7 Entropy, Risk & Comparability
	7.1 Introduction
	7.2 Tail Probabilities and Informational Measures
	7.3 The Conditional Value at Risk
	7.4 Cardinal Versus Ordinal Comparisons
		7.4.1 Utility Theory: A Short Review
		7.4.2 Entropic Asymmetry and Social Utility
	7.5 Information Based Rescaling in Subjectivist Probability
		7.5.1 Formalising as a Change of Measure
		7.5.2 Information Based Rescaling
	7.6 Concluding Remarks: The Scope of Informative Comparisons
	7.7 Literature Notes
	References
Excel VBA Code for the Compressed Smoothing Kernel
Glossary
Index