Everything Is Predictable: How Bayesian Statistics Explain Our World by Tom Chivers

A Predictable World Through a Bayesian Lens

In Everything Is Predictable: How Bayesian Statistics Explain Our World, Tom Chivers takes readers on an intellectual journey into how Bayesian statistics shape our understanding of reality.

He argues that the theory—first introduced in the 18th century by the English clergyman Thomas Bayes—is not merely a dry mathematical tool, but a rational framework for interpreting everything from how the human brain works to contemporary scientific challenges like the replication crisis.

Written in an engaging, narrative style accessible even to non-specialists, the book demonstrates the remarkable explanatory power of Bayesian thinking across fields as diverse as medicine, law, artificial intelligence, and human cognition.

The Man and the Formula – Thomas Bayes and His Enduring Legacy

1.1 The Historical Roots: The Clergyman Who Changed the World

Chivers explores the life of Thomas Bayes (1701–1761), a Nonconformist minister in England and an amateur mathematician.

Bayes never published his theory himself. After his death, his friend Richard Price presented it in a paper titled An Essay Towards Solving a Problem in the Doctrine of Chances. Chivers highlights that Bayes was motivated by a desire to counter the materialist skepticism of his era and to defend a form of rational faith grounded in evidence and inference.

1.2 The Mathematical Formula That Shook the World

Chivers explains Bayes’ theorem in a clear, non-technical way—echoing Stephen Hawking’s famous quip that every equation in a book cuts readership in half.

Bayes’ Theorem:

P(A|B) = \frac{P(B|A) \times P(A)}{P(B)}

Where:

P(A|B) = Posterior probability (the chance that hypothesis A is true given evidence B)
P(B|A) = Likelihood (the chance of seeing evidence B if hypothesis A is true)
P(A) = Prior probability (our belief in A before seeing B)
P(B) = Marginal probability (the chance of observing B under all possible hypotheses)

To illustrate, Chivers uses a classic medical example:

Suppose 1% of women have breast cancer. A mammogram correctly detects cancer 80% of the time but gives false positives 10% of the time. If a woman’s test result is positive, what is the actual probability she has cancer?

Bayesian reasoning shows the chance is only about 7.5%—not 80% as many assume. The low prior probability (1%) has a dramatic effect. This means over 90% of women with positive results would be worried unnecessarily.

The Statistical Camps – Bayesians vs. Frequentists

2.1 Frequentism: A World Without Prior Knowledge

Chivers outlines the frequentist school, which dominated 20th-century statistics. It defines probability as the long-run relative frequency of an event if repeated infinitely. Frequentists use tools like p-values and confidence intervals while treating parameters as fixed but unknown.

The key criticism: this approach ignores prior knowledge or subjective belief, making it rigid when dealing with scarce or complex data.

2.2 Bayesianism: A World of Continuous Updating

By contrast, Bayesian thinking treats probability as a measure of belief or certainty—something we update as new evidence arrives.

Chivers likens this to human learning: we all carry prior assumptions about the world, and as new information emerges, we update our beliefs gradually rather than absolutely.

2.3 The Clash Between the Two

The divide has been so fierce that in the 1970s, Bayesians even sang mocking songs about frequentists at conferences.

For example:

A frequentist says: “If the null hypothesis is true, there’s a 5% chance of seeing these data (p = 0.05).”
A Bayesian says: “Given the data and my prior, I believe this hypothesis is true with probability X%.”

Real-World Applications – From Medicine to AI

3.1 Medical Diagnosis and Decision-Making

Chivers revisits healthcare to show the dangers of statistical misunderstanding.

During the COVID-19 pandemic, the UK considered issuing “immunity passports” based on antibody tests. But ignoring prior probabilities and false positives meant that up to two-thirds of recipients might not have been immune at all, putting themselves and others at risk.

3.2 The Legal System and Forensic Evidence

Bayesian reasoning can also improve justice. Instead of treating DNA matches as absolute proof, jurors could be given likelihood ratios, showing how much more strongly the evidence supports prosecution versus defense claims. This helps avoid the base rate fallacy, which can distort verdicts.

3.3 Algorithms, Spam Filters, and Recommendation Engines

Bayes is also behind everyday technologies. Spam filters use priors (words like “free offer” or “inheritance”) and update with each new message. Similarly, Netflix and Amazon recommendation systems predict what you’ll enjoy next by continuously updating probabilities based on past choices.

Field	Application	How Bayes Works
Medicine	Diagnostic testing	Combines test accuracy (likelihood) with disease prevalence (prior) to estimate true risk (posterior).
Law	Forensic evidence	Compares the probability of evidence if innocent vs. guilty (likelihood ratio).
Technology	Spam filtering	Learns common spam words (priors) and updates with new evidence.
AI & NLP	Machine learning, GPT	Uses priors from training data to predict the next word or action.
Finance	Risk & trading	Updates market models in real time with new financial evidence.

Bayes and Science – From the Replication Crisis to Superforecasting

4.1 Saving Science from the Replication Crisis

Chivers argues that traditional frequentist methods fueled the crisis in psychology and social sciences, where many published results failed to replicate.

Key problems:

P-hacking: chasing p < 0.05 through repeated analyses.
Ignoring priors: giving weak, implausible hypotheses undue weight.
Publication bias: journals favoring “positive” results.

Bayesian solutions:

Bayes Factors to weigh competing hypotheses.
Posterior distributions that quantify uncertainty, not just significance.
Effect sizes instead of binary “statistical significance.”

4.2 The Art and Science of Superforecasting

Chivers discusses the Good Judgment Project, which found “superforecasters” who outperformed experts in predicting geopolitical and economic events.

Their Bayesian-like traits include:

Starting with base rates from history.
Updating beliefs incrementally with new evidence.
Expressing uncertainty numerically (e.g., 60%).
Seeking out contrary evidence to avoid confirmation bias.
Aggregating group forecasts for better accuracy.

The Bayesian Brain – Consciousness as Controlled Hallucination

5.1 The Bayesian Brain Hypothesis

Perhaps the book’s most fascinating section, Chivers argues that the brain itself is a Bayesian machine. Rather than passively receiving sensory input, it actively predicts the world using priors, then corrects based on new evidence.

The gap between prediction and reality—the prediction error—drives learning and perception.

5.2 Perception as Controlled Hallucination

Consciousness, Chivers suggests, is a kind of “controlled hallucination.” What we see, hear, and feel is the brain’s best Bayesian guess about the causes of sensory input.

Optical illusions illustrate this. Take the Necker Cube: the brain flips between interpretations because it tries to impose the most plausible model on ambiguous data.

5.3 Mental Health – When Bayes Breaks Down

Schizophrenia may involve weak priors, leaving sensory input unchecked and producing hallucinations.
Depression may result from overly strong negative priors, resistant to updating even in the face of positive evidence.
Psychedelics may temporarily loosen rigid priors, opening the brain to new models and therapeutic potential.

The Free Energy Principle

Chivers touches on Karl Friston’s Free Energy Principle, which proposes that all living systems—from single cells to societies—aim to minimize prediction error (or “free energy”) by either updating internal models (perception) or altering the environment (action). In this sense, Bayesian reasoning is a biological necessity.

Criticisms and Limits of Bayesian Thinking

Chivers acknowledges that Bayes is no magic bullet:

The Prior Problem: Who decides what priors are reasonable? Different priors can produce starkly different conclusions, fueling political and intellectual polarization.
Overfitting: Bayesian models can become so complex that they fit past data perfectly but fail to predict the future.
Subjectivity: Critics argue that priors inject bias into science, though Bayesians counter that ignoring prior knowledge is itself a subjective choice.

Most statisticians today, Chivers notes, borrow pragmatically from both camps.

Thinking Bayesian in Everyday Life

Chivers closes by offering practical advice for adopting a Bayesian mindset in daily decision-making:

Avoid absolute certainty—never assign 0% or 100% to anything.
Always ask about the base rate before evaluating a situation.
Actively seek disconfirming evidence to counter confirmation bias.
Update your beliefs gradually in proportion to new evidence.
Think in probabilities—assign numbers (20%, 65%) to your judgments for sharper reasoning.

Far more than a statistical guide, this book is a call for intellectual humility, for resisting snap judgments, and for embracing constant updating as we navigate an unpredictable world that nonetheless can be understood more clearly with the right tools.

As Chivers playfully suggests: before reading this summary, you had priors about the book’s quality. Now, with new evidence in hand, it’s time to update them.

For the original summary in Arabic