This is a book about probability and probabilistic reasoning. It is more philosophy than mathematics, but it does have mathematical content and it relies in some measure on mathematical reasoning. The author calls this a “philosophical introduction to uncertainty and the practice of probability, statistics, and modeling of all kinds.” Compared to most people who work in the fields of probability and statistics, the author has fairly extreme views. He’s not the least bit shy about enumerating and expressing them. In short, he argues that:

- All probability is conditional.
- Probability itself is not a decision.

From this position he draws the following conclusions:

- Probability cannot determine a cause.
- Hypothesis tests should be forsaken, as should p-values and Bayes factors.
- Parameters (as in the parameters of a probability model) are usually unobservable and parameter estimation is useless.
- The notion of “statistical significance” should be banished.
- Verified probability models should be used only predictively.

Many experts in probability and statistics could probably find interpretations of several of these statements with which they would agree… up to a point. It is apparent that hypothesis testing is widely misused, and that “p-hacking” has become a serious concern. Some journals will now not accept papers that use p-values. Will we therefore abandon hypothesis testing all together?

This is not the work of a crank. The author has a PhD in statistics; he teaches and works as a statistician. He supports his arguments with clear and careful reasoning presented very deftly. Whether his arguments are convincing is another matter altogether. It is far easier to agree with the author that the interpretation, presentation and communication of statistical results are often highly flawed, and that over-certainty is rampant.

The outline of the author’s argument is, as he suggests, seen most clearly in four chapters in the middle of the book: “Chance and Randomness”, “Causality”, “Probability Models” and “Statistical Models”. The preceding five chapters develop the background on which these are based. The author’s intellectual heroes include Aristotle and Thomas Aquinas, so it’s no surprise that these foundational chapters go back to classical considerations of truth, logic, metaphysics and realism, and the nature of causality.

This book is worth a look by anyone who teaches probability and statistics. If the arguments themselves don’t prove convincing, the cautionary tales that are included are well worth the time.

Bill Satzer (bsatzer@gmail.com) was a senior intellectual property scientist at 3M Company. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.