Publisher Description

Conventional "frequentist" methods that dominate the field of statistics are generally inconsistent and liable to catastrophic failure in some contexts. These weaknesses have become particularly concerning in relation to crises of replicability and credibility in science. Two alternatives have been proposed to address these flaws—classical Bayesian inference and the principle of maximum entropy—but the connections between them remain controversial.

Making Statistics Work presents a synthesis of information theory and Bayesian inference that addresses these fundamental problems. It provides a consistent, powerful, and flexible framework for data inference based on rigorous logic derived from first principles, allowing for new approaches to many of the unresolved questions of statistics. Duncan K. Foley and Ellis Scharfenaker illustrate the application of this framework and the reasoning behind it across a variety of important statistical problems, such as the inference underlying "gold standard" clinical trials, models of human behavior employed in behavioral finance and psychology, analysis of macroeconomic policy, the relationship of classical probability to quantum physics, and the limitations of linear regression analysis. Making Statistics Work offers new insight into contentious topics, from problems of causality and confounding variables in randomized experimental trials to the foundations of Bayesian and frequentist probability theory.

Table of Contents

Part I. Basic Concepts
1. The Statistical Problem
2. Probability
3. Probabilities and Information
4. Likelihoods and Data
5. Priors and Constraints
6. Organizing Statistical Inference
Part II. Multinomial Models
7. The Binomial Model for Repeated Bernoulli Trials
8. The Multinomial Model
9. The Quantal Response Model
10. Fourier Transforms and Time Series
11. Complex Amplitudes as Multinomial Parameters
Part III. Real Number Observations
12. Real Scalar Statistics
13. Real Vector Statistics
Part IV. Advanced Topics
14. Constrained Maximum Entropy
15. Confounding Variables and Limited Information
Part V. Philosophical and Methodological Puzzles
16. De Finetti's Economic Model of Probability
17. The Frequency Model of Probability
18. Mathematical Appendix
Notes
Bibliography
Author Index
Subject Index

Review

At last, a statistics book that engages the philosophical foundations of probability and fully develops their implications through to practice. Clear, rigorous, and refreshingly honest about assumptions, it sets a new standard and should be required reading for anyone serious about statistics. -- Aubrey Clayton, author of Bernoulli's Fallacy: Statistical Illogic and the Crisis of Modern Science
In Making Statistics Work, Duncan K. Foley and Ellis Scharfenaker combine information theory, Bayesian updating, and probability theory into a single logical framework for statistical inference under imperfect and insufficient information. The authors provide many examples, making the book very accessible. This is a valuable resource for scientists, students, and teachers across disciplines. -- Amos Golan, American University and the Santa Fe Institute
Making Statistics Work introduces a robust framework that brings together information theory and Bayesian inference through entropy-maximizing priors. Offering both readability and rigor, this book is a refreshing alternative to the conventional statistical education. -- Jangho Yang, University of Waterloo

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