I. J. Good was a polymath who made notable contributions to mathematics, physics, computer science, philosophy, and especially statistics. He is particularly well known as an advocate for hierarchical Bayesian statistics, but he was a moderate and a compromiser in the battles between Bayesians and anti-Bayesians. He was also a co-discoverer of the Fast Fourier Transform in its prime-factor form. His was a mind bursting with ideas, good and bad, and he never attended to the ephemeral boundaries between disciplines.
The current book is a republication by Dover of a 1983 book that is a collection of articles, mostly on probability and statistics, with an emphasis on foundational questions. Good says that his book is about “applicable philosophy,” which for him includes “philosophy, probability, statistics and mathematics.” In general the individual articles tend to be more philosophical and less mathematical. Most of the articles in the book are based on invited lectures. An overall theme throughout is the value of rational thinking based on the principles of probability.
The book is divided into five parts. The first, titled “Bayesian Rationality,” discusses the maximization of expected utility. Good has a predilection for counting things; one article enumerates twenty-seven principles of rationality, another 46,656 varieties of Bayesians. (Good also kept careful track of his “main publications,” at least up to the time of this book, assigning them each a number and then sometimes citing them only by number. There are more than 1500.)
The second section includes a small collection of articles on probability that begins with the question whether probability or statistics is historically or logically prior. (Good concludes that it’s a chicken and egg situation.) Another article in this section thoughtfully examines the place randomness plays in statistics.
The third section focuses on hypothesis testing and corroboration. As an example of a Bayesian approach to physical “numerology,” Good asks how we should regard a theory like Bode’s law (a formula predicting the distance from the sun of bodies in the solar system that may be purely coincidental). The fourth part considers information, surprise and (therefore) entropy. The final part discusses explanation and causality and proposes a “causal calculus”.
This is a charming collection by a gifted and prolific thinker. Selected pieces would serve well as supplemental reading for advanced undergraduate courses in probability and statistics.
Bill Satzer (firstname.lastname@example.org) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.
|Part I. Bayesian Rationality|
|1. Rational Decisions|
|2. Twenty-seven Principles of Rationality|
|3. 46656 Varieties of Bayesians|
|4. The Bayesian Influence, or How to Sweep Subjectivism under the Carpet|
|Part II. Probability|
|5. Which Comes First, Probability or Statistics|
|6. Kinds of Probability|
|7. Sublective Probability as the Measure of a Non-measurable Set|
|8. Random Thoughts about Randomness|
|9. Some History of the Hierarchical Bayesian Methodology|
|10. Dynamic Probability, Computer Chess, and the Measurement of Knowledge|
|Part III . Corroboration, Hypothesis Testing, Induction, and Simplicity|
|11. The White Shoe is a Red Herring|
|12. The White Shoe qua Herring is Pink|
|13. A Sublective Evaluation of Bode's Law and an "Objective" Test for Approximate|
|14.Some Logic and History of Hypothesis Testing|
|15. Explicativity, Corroboration, and the Relative Odds of Hypothesis|
|Part IV Information and Surprise|
|16. The Appropriate Mathematical Tools for Describing and Measuring Uncertainty|
|17. On the Principle of Total Evidence|
|18.A Little Learning Can Be Dangerous|
|19. The Probabilistic Explication of Information, Evidence, Surprise, Causality,|
|Explanation, and Utility|
|20. Is the Size of Our Galaxy Surprising?|
|Part V. Causality and Explanation|
|21. A Causal Calculus|
|22. A Simplification in the "Causal Calculus"|
|23. Explicativity: A Mathematical Theory of Explanations with Statistical Applications|
|Sublect Index of the Bibliography|