(p. A13) First articulated in the 18th century by a hobbyist-mathematician seeking to reason backward from effects to cause, Bayes’ theorem spent the better part of two centuries struggling for recognition and respect. Yet today, argues Tom Chivers in “Everything Is Predictable,” it can be seen as “perhaps the most important single equation in history.” It drives the logic of spam filters, artificial intelligence and possibly our own brains. . . .
At its core, the theorem provides a quantitative method for getting incrementally wiser by continuously updating what you think you know—your prior beliefs, which initially might be subjective—with new information. Your refined belief becomes the new prior, and the process repeats.
. . .
At times Mr. Chivers, a London-based science journalist who now writes for Semafor, seems overwhelmed by an admittedly complex subject, and his presentation lacks the clarity of Sharon Bertsch McGrayne’s “The Theory That Would Not Die” (2011). Yet he is onto something, since Bayes’ moment has clearly arrived. He notes that Bayesian reasoning is popular among “people who come from the new schools of data science—machine learning, Silicon Valley tech folks.” The mathematician Aubrey Clayton tells him that, in the cutting-edge realms of software engineering, “Bayesian methods are what you’d use.”
. . .
It’s notoriously difficult for most people to grasp problems in a structured Bayesian fashion. Suppose there is a test for a rare disease that is 99% accurate. You’d think that, if you tested positive, you’d probably have the disease. But when you figure in the prior—the fact that, for the average person (without specific risk factors), the chance of having a rare disease is incredibly low—then even a positive test means you’re still unlikely to have it. When quizzed by researchers, doctors consistently fail to consider prevalence—the relevant prior—in their interpretation of test results. Even so, Mr. Chivers insists, “our instinctive decision-making, from a Bayesian perspective, isn’t that bad.” And indeed, in practice, doctors quickly learn to favor common diagnoses over exotic possibilities.
. . .
Our brains work by making models of the world, Mr. Chivers reminds us, assessing how our expectations match what we earn from our senses, and then updating our perceptions accordingly. Deep down, it seems, we are all Bayesians.
For the full review, see:
(Note: the online version of the review has the date May 14, 2024, and has the title “‘Everything Is Predictable’ Review: The Secret of Bayes.” In the last quoted sentence I have replaced the word “earn” that appears in both the online and print versions, with the word “learn.”)
The book under review is:
Chivers, Tom. Everything Is Predictable: How Bayesian Statistics Explain Our World. New York: Atria/One Signal Publishers, 2024.