Bowden R. The Information Theory of Comparisons. With Applications to Statistics and the Social Sciences

New York: Springer, 2018. — 169 p.This book finds a broad domain of relevance in statistics and the social sciences. Its conceptual development is supported by applications to economics and income distribution, finance, education, demographics and actuarial science, political studies, psychology, and general statistics.
Fresh perspectives on directional complexity have generated an informational theory of ‘more versus less’, with representative polar outcomes as good or bad, or rich or poor. New duality metrics for spread and asymmetry have resulted, motivated by internal perspectives on the part of subjects, such as attitudes to their comparative (dis)advantage. This book is a readable review of these developments. Concepts and applications are described in tandem with each other. They consolidate recent contributions to the research literature, augmented with fresh insights and applications. Dynamic extensions include modeling shifting social attitudes, while the broader agenda encompasses topical areas such as subjectivist probability, investment decision making, and income distribution.Information, Complexity and Entropy
Entropic Decompositions
Partition Entropy
Complexity and the Psychology of Investment Decisions
An Extension: The Frequency Domain
Partition Entropy and the Log Odds Function
Discrete Valued Random Variables and Histograms
Resolving Grade Uncertainty
Tail Complexity and Market Clearing Prices
Literature NotesLeft and Right Entropic Shifts
Shift Kernels: Concentrators and Spreaders
Some Extensions
Perspectives on Mixture Distributions
The Entropic Kernel: Data Smoothing and End Correction
End Correction with Kernel Compression
The Social Dynamics of Opinion
The Momentum of Opinion
Application of Mixture Theory to Value at Risk
Literature NotesMoments for the Entropic Shifts
The Double Smoothing Property
Asymmetry and Spread Functions
Summary Metrics for Asymmetry and Spread
Gini’s Mean Absolute Difference and Welfare Variants
The Economic Dynamics of Remuneration Relativities
Relationship with Stochastic Dominance
Literature NotesIncome Distribution
Implementation as Entropic Asymmetry and Spread Metrics
Social Welfare Aspects
Dynamics: The v-d Phase Plane
Application to Stock Market Performance
Actuarial Life Expectancy
Literature NotesA First Approach Based on Spanning
Bipolarity: The Entropic Centre and Equivalent Width
Polar Asymmetry and Spread Metrics
Fund Performance Measures
Actuarial Uncertainty RevisitedHigher Dimensions: Directional Shifting Perspectives
Left and Right Hand Smoothing Moments
Co-smoothing
Index Combinations
Co-smoothing and the Ordered Mean Difference
The OMD in Context: Some Financial Decision Theory
Do Hedge Funds Really Add Value?
Literature NotesTail Probabilities and Informational Measures
The Conditional Value at Risk
Utility Theory: A Short Review
Entropic Asymmetry and Social Utility
Information Based Rescaling in Subjectivist Probability
Formalising as a Change of Measure
Information Based Rescaling
Concluding Remarks: The Scope of Informative ComparisonsExcel VBA Code for the Compressed Smoothing Kernel