Everything Is Predictable: How Bayesian Statistics Explain Our World in Science and Inquiry

Jul 16, 2025 Tomislav rated it liked it

Shelves: mathematics, science

“The Fox knows many things – the hedgehog one big one” -Archilochus. Tom Chivers has the big idea that Bayesian epistemology explains everything. Not just numerical decision theory, as in Thomas Bayes’ actual equation (See the book cover.), but many aspects of our lives from sociology down through homeostatic biological systems. And it’s true that if you boil Bayes down to the basic prior assumption/acquire data/posterior assumption cycle of a feedback loop, you can find it almost everywhere. I “The Fox knows many things – the hedgehog one big one” -Archilochus. Tom Chivers has the big idea that Bayesian epistemology explains everything. Not just numerical decision theory, as in Thomas Bayes’ actual equation (See the book cover.), but many aspects of our lives from sociology down through homeostatic biological systems. And it’s true that if you boil Bayes down to the basic prior assumption/acquire data/posterior assumption cycle of a feedback loop, you can find it almost everywhere. I feel it would be better to think of Bayes Equation as a numerical tool describing predictive probabilities rather than a universal principle. The book is at its strength on Decision Theory (chapter 3) and its weakest on Brain Science (chapter 5).

I read this book to learn, and am not expert in the subject, and so would be interested in hearing the thoughts of other readers to the criticisms I’ve raised in each chapter. Finally, I’ve noted a few errata that I feel are due to bad editing, that really slowed down my understanding while I tried determine if it was him or me.

Introduction “A Theory of Not Quite Everything”. The gist of the title is that everything is predictable, so long as we understand that prediction is not predestination, but an evaluated probability. This introduction is a teaser, giving the equation and describing the many fields in which Bayesian statistics are relevant, but without really explaining it.

Chapter One “From The Book of Common Prayer to the Full Monte Carlo”. Thomas Bayes was a British 18th century Presbyterian minister and amateur mathematician, some of whose work was published posthumously. Chivers gives a biographical narrative that relates Bayes’ innovative statistical thinking to his Nonconformist theology. I needed to do a little outside reading and found that Non-Conformism was a catch-all for various schools of Christian Protestant thought, that were outside the Church of England orthodoxy. Chivers gives history of the subtle philosophical difference between Bayesian and “frequentist” statistics, and of the rivalry between proponents of each, with some explaining along the way. The author seems to be a Bayesian partisan himself, as the descriptions of “frequentist” formulation are less lucid. Perhaps he is assuming we are already well-schooled in that.

Chapter Two “Bayes in Science”. This chapter emphasizes the philosophical distinction in the meaning of p-value. It is not the likelihood of the truth of the hypothesis given the data, but likelihood of the data given the hypothesis. To me, this seems more important in the less deterministic sciences, where p-value thresholds might be .05 - such as sociology, psychology, medicine. Chivers’ writing takes on a pedantic tone. When the non-Bayesian Daniël Lakens describes the meaning and use of frequency statistics in the philosophy of science, Chivers thinks he is being “implicitly Bayesian.” I guess it is easier to argue against a position that YOU have restricted to a purer form that its owners do. Note correction on page 140. Misconception. The aerodynamic theory used in the example is solely applicable to gliders. Propelled air vehicles also have rocket-like dynamics. Note correction on page 153, line 1. Editing error. You multiply prior and likelihood together, not posterior and likelihood.

Chapter Three “Bayesian Decision Theory”. Most of the chapter consists of an explanation and examples of decision theory that anyone who has written software will readily understand. Near the end, he brings up the topic of AI, which he casts into a Bayes framework. It seems an attempt to bring a popular topic under his own umbrella. As he admits, “As you can imagine, you can model this is a Bayesian way even if the AI isn’t explicitly running Bayes under the hood.”

Chapter Four “Bayes in the World”. This chapter is about using a Bayesian orientation as a method of epistemology. Many people make inaccurate predictions. Chivers says this can be improved by assigning probabilities to priors, even in questions which appear not easily quantifiable, and then incorporating observed information. He opens with some examples of how humans sometimes misapply learned heuristics. Some of the examples, including the familiar Monty Hall three doors scenario, which I last saw in Mlodinow’s The Drunkard's Walk: How Randomness Rules Our Lives, seem to be cases of how to count the states of independent variables. By the end, his theme has generalized into how to think more systematically in a non-binary way about prediction. Note correction on page 232-3, example. Editing error. If each card has either a number or a letter on one side, and either a person or an animal of the other side, then no card should be having a star. Note correction on page 233, line 5. Editing error. The claim is about numbers and animals, not squares and animals.

Chapter Five “The Bayesian Brain”. I think he is attempting to explain human perception in Bayesian terms, and perhaps it is so in a conceptual way. But the explanations seem muddled. Is he talking about perception, or conscious decision making, or both at the same time? In defining a theory of a top-down stream of information, he writes about sending electrical signals down from brain to nerve receptors, breaking down of composite forms into more elementary forms, and “higher-level parts” of the brain to “lower-level parts”, all in the same description. It seems a model of human perception envisioned as a hierarchical network of computers. But is that the biology? By the end of the chapter, he cites a somewhat sketchy description of the brain’s more automatic functions to be corrections on bad prior assumptions of lack of function. Homeostasis would be better understood as a negative feedback cycle.

Conclusion “Bayesian Life”. Reiterate and wrap up. ...more

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Dec 15, 2024 CatReader rated it liked it

2.5 stars. If you've never read a book on Bayesian statistics, this book may be of interest to you -- but if you have (like me), you may find yourself bored to tears through science writer Tom Chivers' prolonged biography of Thomas Bayes and recapitulation of the theorem, extended philosophical musings, and various tangents on other topics like perception.

Further reading:
Rigor Mortis: How Sloppy Science Creates Worthless Cures, Crushes Hope, and Wastes Billions by Richard Harris (my absolute fav ...more

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Sep 13, 2025 John McPhee rated it it was amazing · review of another edition

Wow. This is not a fast or light read. Came highly recommended so I plowed through. Great examples. Smart conclusions. I liked the idea of quantifying and structuring the reality of LLL (life-long learning) … and did not know that Bayes had done this work. If LLL is also you the this may be a valuable read for you. It was for me. (This summary below was a review out on www that I liked and agreed with).

At its core, the theorem provides a quantitative method for getting incrementally wiser by co Wow. This is not a fast or light read. Came highly recommended so I plowed through. Great examples. Smart conclusions. I liked the idea of quantifying and structuring the reality of LLL (life-long learning) … and did not know that Bayes had done this work. If LLL is also you the this may be a valuable read for you. It was for me. (This summary below was a review out on www that I liked and agreed with).

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.

The essential concept was developed by Thomas Bayes, a Presbyterian minister in Britain, and rescued from oblivion by his friend Richard Price, who published it in 1763. The work “sunk almost without trace,” Mr. Chivers says, until it was independently discovered and refined in 1774 by the French polymath Pierre-Simon Laplace.

Before the theorem and its broader pattern of reasoning could gain much traction, Mr. Chivers explains, it was overtaken by approaches that felt less “soft and squishy.” In the early 19th century, for example, Belgian prodigy Adolphe Quetelet began measuring anything that could be objectively quantified, like the chest size of Scottish soldiers. His interest was “social physics”—using the rigors of mathematics to improve society.

In the early 20th century, the charge to treat data hermetically was led by two British scholars, Karl Pearson and R.A. Fisher, who despised subjectivity, Bayesian reasoning and each other. The analytical methods they developed—particularly the concept of “statistical significance”—are ubiquitous in scientific publications today, representing a core principle of what is now known as “frequentist statistics.” In this framework, the analysis relies strictly on observed data, independent of prior beliefs. Bayesian statistics, by contrast, dynamically update beliefs about a hypothesis as more data become available.

Despite the “furious rejection of Bayesianism” by Fisher and his colleagues, Mr. Chivers says, “people kept rediscovering or reinventing it, because it kept working.” Harold Jeffreys, a Cambridge geologist, used it to assess Earth’s composition; insurance underwriters used it to set premiums for workplace liabilities; artillery commanders used it to aim projectiles. Even as the techniques of Pearson and Fisher became enshrined in statistics departments, a rebellious community of Bayesians persisted on the fringes, devouring books that were “passed down almost like samizdat,” as Mr. Chivers puts it. In 1979, the dispersed Bayesian community convened in Valencia, Spain, for a conference that would become a quadrennial tradition, famous for late-night singalongs featuring alcohol-infused statisticians warbling “There’s no theorem like Bayes’ theorem” and “Then I saw Tom Bayes, now I’m a believer.”

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.”

Bayes’ theorem is considered essential for decision-making under conditions of uncertainty. It’s used when a radiology AI identifies a cancer and when ChatGPT composes a story. If there is a problem, Mr. Chivers suggests, it is that we don’t use Bayesian reasoning often enough. It could improve the quality of scientific literature by giving researchers a “vehicle for skepticism.” It might also help us make better predictions. The “superforecasters” identified by the political psychologist Philip Tetlock use a Bayesian approach, establishing priors, tracking their results and revising their assumptions as they attempt to predict events such as currency moves and election results.

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.

Bayesian reasoning also reminds us that when doctors encounter patient preferences that seem irrational (refusing childhood vaccines comes to mind), they should focus on identifying the underlying beliefs, since it’s likely the priors that are dubious, not the reasoning that follows. Relatedly, Mr. Chivers notes, depression may result from “inappropriately strong priors on some negative belief.” The promise of psychedelic medicines like psilocybin could lie in their ability to “flatten” these priors and help patients access a balanced worldview.

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. ...more

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Jul 13, 2024 taylor rated it it was amazing

I was on the struggle bus for most of this read. The central theme is Bayes Theorem. The classic example is as follows

Approximately 1% of women aged 40-50 have breast cancer. A woman with breast cancer has a 90% chance of a positive test from a mammogram, while a woman without has a 10% chance of a false positive result. What is the probability a woman has breast cancer given that she just had a positive test?

This example is copied from https://pi.math.cornell.edu/~mec/2008...
The other example r ...more

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