Introduction: A theory that explains quite a bit.

Chapter 1: From the Book of Common Prayer to Nude Performances

The Life of Thomas Bayes | Pascal and Fermat | The Law of Large Numbers | De Moivre and the Normal Distribution | Simpson and Bayes | Bayes's Billiard Table | The First Bayesian Defends God Against Hume | From Bayes to Galton | Galton, Pearson, Fisher, and the Rise of Frequentism | Are Frequentists Racists? | The Fall of Bayesianism | Statistical Significance | Bayes in Crisis | Glory, Glory, Probability

Chapter 2: Bayes in Science

The Reproducibility Crisis in Science and Solutions | Superpowers, a Moon Made of Cheese, and Faster-than-Light Particles | Popper's Swan | Bayes and the Reproducibility Crisis | Dennis Lindley's Paradox | Finding Prior Probabilities | The Unfinished Debate

Chapter 3: Bayesian Decision Theory

Aristotle and George Boole | Bayes's Law: The Core of Decision Making | Cromwell's Law | The Law of Conservation of Expected Evidence | Utility, Dutch Book, and Game Theory | Occam's Prior | Super-Prior Probability | Multiple Hypotheses | AI and Bayes

Chapter 4: Bayes in the World

Are Humans Irrational? | Monty's Difficult Bargain | The Superforecaster (Part 1) | The Superforecaster (Part 2) | Bayesian Epistemology

Chapter 5: Bayesian Brain Model

From Plato to Gregory | Optical Illusions | Reality is a Controlled Hallucination | Dopamine and Advanced Computer Robots | Waddle, Tennis, and Rapid Eye Movement | Why People with Schizophrenia Can Tickle Themselves | Have You Ever Taken a Good Look at Your Hands? | God, Please

Conclusion: Bayes in Life

Acknowledgements
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The only book on Bayes' theorem written by a master of statistics for the masses.
Royal Statistical Society Award for Excellence in Statistics in Journalism
A new book from Tom Chivers, winner of this year's Science Writer of the Year award.

★★★Finalist for the Royal Society Scientific Book Award★★★
★★★Amazon Math Bestseller★★★
★★★Recommended by Kim Beom-jun, Philip Ball, Tim Harford, and Will Stowe★★★

“A wonderful book for anyone who wants to see through a world that seems opaque.”
Kim Beom-jun (Professor of Physics, Sungkyunkwan University)

"Can you predict the future? Of course you can!"
The one and only solution to the uncertainty of the future
The Science of Prediction: Understanding Bayes' Theorem

As the new year approaches, many people begin to envision an uncertain future for themselves.
In fact, our lives are a series of big and small predictions from beginning to end.
We make basic, implicit predictions, such as that the sun will rise tomorrow morning or that we will soon inhale and exhale.
We also make more complex predictions, like whether a friend we're meeting will be on time or whether the convenience store will still have our favorite orange juice.
Furthermore, predictions are made based on a myriad of factors, such as weather, climate, and the economic situation decades into the future.
All predictions share a common characteristic: uncertainty. However, our ability to roughly predict the world and navigate it is not due to some mystical power of foresight, but rather to the information we have gathered in the past.
A powerful tool to help us make the best decisions with such limited information is Bayes' theorem.


Bayes' theorem is a theory discovered by the 18th-century British amateur mathematician Thomas Bayes, and is a powerful principle that allows us to more accurately predict the probability of an event based on the information we have.
Although it seems simple, this theorem is a key tool in many fields today, from spam filters to legal systems, medical diagnosis, neuroscience, and artificial intelligence.
Especially in today's data-saturated world, this discipline is essential for reducing uncertainty and making reliable decisions.
Bayes' theorem is not just a useful tool, it's also the way our minds and consciousness work.
This book briskly explains the concepts, controversies, and philosophical implications of Bayes' theorem, using familiar, everyday examples, guiding readers to view the world more rationally.

“If geometry has the Pythagorean theorem, probability theory has Bayes’ theorem.”
The most important formula in history that everyone should understand
Essential knowledge for the big data era, even without mathematical knowledge

A positive result was obtained in a cancer diagnostic test that has a sensitivity of 80 percent, meaning that it correctly predicts that a person with the disease has the disease.
What's the probability of having cancer? 80 percent? No.
The reason is Bayes' theorem.
Bayes' theorem is expressed as P(A|B)=P(B|A)×P(A)/P(B), which calculates the probability that event A occurs given that event B has occurred.
In the case of diagnostic testing, what we want to know is, 'If the test result is positive, what is the probability that I have cancer?'
However, what 'sensitivity' tells us is the exact opposite information: 'the probability that the test result will be positive when you have cancer.'
Although they sound similar, they have completely different meanings.
It's like saying, "The probability of any human being being the Pope is 1 in 8 billion" and "The probability of the Pope being human is 1 in 8 billion" are completely different statements.
To properly understand this difference, we need additional information about the prevalence, or what Bayes' theorem calls the "prior probability."
If the prevalence of that cancer is, say, 1 percent, then the probability that I actually have cancer may only be 7 percent.


In this way, Bayes' theorem serves as the most rational standard for decision-making in uncertain situations, such as not only medical diagnosis but also the scientific activity of establishing and verifying hypotheses, and forensic activities such as determining the likelihood of a suspect being the criminal based on DNA test results.
Bayes' theorem also raises philosophically interesting questions.
What is probability? Is the statement, "The probability of getting heads when flipping a coin is 1/2," an objective fact about the world? Bayes' theorem interprets probability not as a fixed property of the objective world, but rather as a subjective belief that varies depending on the observer.
But being subjective doesn't mean it's baseless or random.
Rather, Bayes' theorem suggests a way to make the most of the information and data we have to reach rational conclusions.


“Everything is a prediction, and what’s interesting is the prediction error.”
From diagnostic tests to how the brain works,
A single textbook on Bayes' theorem

The book unfolds in five themes how Bayes' theorem, a one-line mathematical formula, can be a powerful tool for explaining the world and understanding ourselves.
Chapter 1 introduces the life of Thomas Bayes, an 18th-century amateur mathematician and clergyman, and the birth of Bayes' theorem.
It illuminates the conflict between frequentism and Bayesianism that arose during the development of statistics, and also provides an interesting explanation of how the history of probability and statistics, which began with gambling such as dice and cards, is intertwined with racism such as eugenics.


Chapter 2 explores the role of probability and statistics in scientific research, focusing on the "reproducibility crisis" that shook the scientific community.
In 2011, American social psychologist Daryl Behm published a paper arguing that "precognition exists."
Although it was contrary to common sense, it was a 'scientifically significant' result derived using the correct methodology and tools.
Similarly, a "reproducibility crisis" has emerged in psychology, particularly as a number of high-profile research findings have failed to replicate in repeated experiments.
This crisis has clearly demonstrated how frequentist statistics can undermine the reliability of research results.
The author shows how Bayesianism can solve or complement these problems and highlights the advantages of Bayesian methodology.


Chapter 3 explains specifically why Bayes' theorem is essential in decision theory.
In particular, it covers how Bayes' theorem operates as a core principle of decision-making in artificial intelligence and game theory.
Reading explanations of Cromwell's law, which states that nothing should be given a 100% or 0% probability other than a proposition that is logically either true or false, or the multiple hypothesis problem, which shows that even claims that are unwavering in the face of clear evidence, like vaccine conspiracy theories, can be the product of rational reasoning, reveals the crucial role Bayes' theorem plays in decision theory.

Chapter 4 covers Bayesian inference in everyday life.
It seems that humans are prone to making irrational judgments due to various errors and biases, but it emphasizes that in reality, they make rational decisions that are closer to Bayesian thinking.
In a prediction study involving a large number of experts, including journalists, military commanders, politicians, and academics, as well as famous quizzes like the 'Monty Hall Problem,' the average forecaster's performance was no better than that of a 'dart-throwing chimpanzee,' while the secrets of 'superforecasters' who showed outstanding prediction skills are also covered.


Chapter 5 explains how our brain works, and that perception and consciousness itself are Bayesian.
Through various examples of optical illusions, such as the bizarre 'concave mask' illusion and the 'dress illusion' that took the internet by storm for a while, as well as perceptual processes and mental illness, the Bayesian process by which the brain makes predictions and corrects them is explored.
In particular, it suggests that mental illnesses such as schizophrenia and depression can be explained by errors in the prediction process, providing new insights into human consciousness.


“I beg you to consider the possibility that you are wrong.”
Why it's important to renew your beliefs based on new evidence

From spam filtering to evolution, everything related to decision-making, science—the highest level of human thought—and even how the brain itself works, Bayes' theorem is a powerful and useful tool for explaining the world.
The author suggests important lessons we can learn from this summary.
First, I say that there is no need to be bound by dichotomous thinking such as right/wrong, true/false.
Because in the real world, such clear boundaries often do not exist.
The same goes for debates surrounding vague and ambiguous categorical definitions like, "Is Party A a fascist organization?", "Is Group B a cult?", or "Is Person C a racist?"
Instead of this approach, we can adjust the strength of our beliefs through probabilistic thinking.

Updating our knowledge in light of new evidence is central to Bayesian thinking, and this attitude leads to rational judgment.
This helps us avoid falling into superficial postmodern relativism even when faced with uncertainty, reduces prediction errors, and builds the most robust beliefs.
This book is not simply a book that covers one field of mathematics.
Bayes' theorem embodies the ability to renew beliefs and deal with uncertainty through probabilistic thinking.
As we seek to view the world more rationally and learn how to live wisely in the midst of a deluge of information, Bayes' theorem will be an essential compass and map.