Bayesian Investor Blog

Book review: Everything Is Predictable: How Bayesian Statistics Explain Our World, by Tom Chivers.

Many have attempted to persuade the world to embrace a Bayesian worldview, but none have succeeded in reaching a broad audience.

E.T. Jaynes’ book has been a leading example, but its appeal is limited to those who find calculus enjoyable, making it unsuitable for a wider readership.

Other attempts to engage a broader audience often focus on a narrower understanding, such as Bayes’ Theorem, rather than the complete worldview.

Claude’s most fitting recommendation was Rationality: From AI to Zombies, but at 1,813 pages, it’s too long and unstructured for me to comfortably recommend to most readers. (GPT-4o’s suggestions were less helpful, focusing only on resources for practical problem-solving).

Aubrey Clayton’s book, Bernoulli’s Fallacy: Statistical Illogic and the Crisis of Modern Science, only came to my attention because Chivers mentioned it, offering mixed reviews that hint at why it remained unnoticed.

Chivers has done his best to mitigate this gap. While his book won’t reach as many readers as I’d hoped, I’m comfortable recommending it as the standard introduction to the Bayesian worldview for most readers.

Basics

Chivers guides readers through the fundamentals of Bayes’ Theorem, offering little that’s extraordinary in this regard.

A fair portion of the book is dedicated to explaining why probability should be understood as a function of our ignorance, contrasting with the frequentist approach that attempts to treat probability as if it existed independently of our minds.

The book has many explanations of how frequentists are wrong, yet concedes that the leading frequentists are not stupid. Frequentism’s problems often stem from a misguided effort to achieve more objectivity in science than seems possible.

The only exception to this mostly fair depiction of frequentists is a section titled “Are Frequentists Racist?”. Chivers repeats Clayton’s diatribe affirming this, treating the diatribe more seriously than it deserves, before dismissing it. (Frequentists were racist when racism was popular. I haven’t seen any clear evidence of whether Bayesians behaved differently).

The Replication Crisis

Chivers explains frequentism’s role in the replication crisis.

A fundamental drawback of p-values is that they indicate the likelihood of the data given a hypothesis, which differs from the more important question of how likely the hypothesis is given the data.

Here, Chivers (and many frequentists) overlook a point raised by Deborah Mayo: p-values can help determine if an experiment had a sufficiently large sample size. Deciding whether to conduct a larger experiment can be as crucial as drawing the best inference from existing data.

The perversity of common p-value usage is exemplified by Lindley’s paradox: a p-value below 0.05 can sometimes provide Bayesian evidence against the tested hypothesis. A p-value of 0.04 indicates that the data are unlikely given the null hypothesis, but we can construct scenarios where the data are even less likely under the hypothesis you wish to support.

A key factor in the replication crisis is the reward system for scientists and journals, which favors publishing surprising results. The emphasis on p-values allows journals to accept more surprising results compared to a Bayesian approach, creating a clear disincentive for individual scientists or journals to adopt Bayesian methods before others do.

Minds Approximate Bayes

The book concludes by describing how human minds employ heuristics that closely approximate the Bayesian approach.

This includes a well-written summary of how predictive processing works, demonstrating its alignment with the Bayesian worldview.

Concluding Thoughts

Chivers possesses a deeper understanding of probability than many peer-reviewed journals. He has written a reasonably accessible description of it, but the subject remains challenging. While he didn’t achieve the level of eloquence needed to significantly increase the adoption of the Bayesian worldview, his book represents a valuable contribution to the field.

Obligatory XKCD: