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Everything Is Predictable: How Bayesian Statistics Explain Our World
A captivating and user-friendly tour of Bayes’s theorem and its global impact on modern life from the acclaimed science writer and author of The Rationalist’s Guide to the Galaxy .
At its simplest, Bayes’s theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. But in Everything Is Predictable, Tom Chivers lays out how it affects every aspect of our lives. He explains why highly accurate screening tests can lead to false positives and how a failure to account for it in court has put innocent people in jail. A cornerstone of rational thought, many argue that Bayes’s theorem is a description of almost everything.
But who was the man who lent his name to this theorem? How did an 18th-century Presbyterian minister and amateur mathematician uncover a theorem that would affect fields as diverse as medicine, law, and artificial intelligence?
Fusing biography, razor-sharp science writing, and intellectual history, Everything Is Predictable is an entertaining tour of Bayes’s theorem and its impact on modern life, showing how a single compelling idea can have far reaching consequences.
At its simplest, Bayes’s theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. But in Everything Is Predictable, Tom Chivers lays out how it affects every aspect of our lives. He explains why highly accurate screening tests can lead to false positives and how a failure to account for it in court has put innocent people in jail. A cornerstone of rational thought, many argue that Bayes’s theorem is a description of almost everything.
But who was the man who lent his name to this theorem? How did an 18th-century Presbyterian minister and amateur mathematician uncover a theorem that would affect fields as diverse as medicine, law, and artificial intelligence?
Fusing biography, razor-sharp science writing, and intellectual history, Everything Is Predictable is an entertaining tour of Bayes’s theorem and its impact on modern life, showing how a single compelling idea can have far reaching consequences.
384 pages, Hardcover
First published April 25, 2024
About the author
Tom Chivers
15 books33 followersTom Chivers is a writer, publisher and arts producer. He was born in 1983 in south London.
He has released two pamphlets of poetry, The Terrors (Nine Arches Press, 2009; shortlisted for the Michael Marks Award) and Flood Drain (Annexe Press, 2012), and two full collections, How To Build A City (Salt Publishing, 2009) and Dark Islands (Test Centre, 2015). His poems have been anthologised in Dear World & Everything In It (Bloodaxe Books, 2013) and London: A History in Verse (Harvard University Press, 2012).
His non-fiction debut London Clay: Journeys in the Deep City will be published by Transworld/Doubleday in September 2021. He is represented by Sophie Scard at United Agents.
‘Chivers’s writing feels refreshing and necessary, a genuine, lyrical appraisal of contemporary life.’
Luke Kennard, Poetry London
Tom won an Eric Gregory Award in 2011 and was shortlisted for the Edwin Morgan Prize in 2014. He has performed at numerous events and venues including Dasein Poetry Festival, Athens; The Eden Project, Cornwall; Ledbury Poetry Festival; London Literature Festival; Moray Walking Festival; Poetry International; The Sage Gateshead; Soho Theatre and The Thames Festival.
Tom has made perambulatory, site-specific and audio work for organisations including LIFT, Cape Farewell, Humber Mouth Literature Festival, Outpost London and Southbank Centre. He lives in Rotherhithe with his wife and two daughters.
He has released two pamphlets of poetry, The Terrors (Nine Arches Press, 2009; shortlisted for the Michael Marks Award) and Flood Drain (Annexe Press, 2012), and two full collections, How To Build A City (Salt Publishing, 2009) and Dark Islands (Test Centre, 2015). His poems have been anthologised in Dear World & Everything In It (Bloodaxe Books, 2013) and London: A History in Verse (Harvard University Press, 2012).
His non-fiction debut London Clay: Journeys in the Deep City will be published by Transworld/Doubleday in September 2021. He is represented by Sophie Scard at United Agents.
‘Chivers’s writing feels refreshing and necessary, a genuine, lyrical appraisal of contemporary life.’
Luke Kennard, Poetry London
Tom won an Eric Gregory Award in 2011 and was shortlisted for the Edwin Morgan Prize in 2014. He has performed at numerous events and venues including Dasein Poetry Festival, Athens; The Eden Project, Cornwall; Ledbury Poetry Festival; London Literature Festival; Moray Walking Festival; Poetry International; The Sage Gateshead; Soho Theatre and The Thames Festival.
Tom has made perambulatory, site-specific and audio work for organisations including LIFT, Cape Farewell, Humber Mouth Literature Festival, Outpost London and Southbank Centre. He lives in Rotherhithe with his wife and two daughters.
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Displaying 1 - 30 of 44 reviews
May 1, 2024
There's a stereotype of computer users: Mac users are creative and cool, while PC users are businesslike and unimaginative. Less well-known is that the world of statistics has an equivalent division. Bayesians are the Mac users of the stats world, where frequentists are the PC people. This book sets out to show why Bayesians are not just cool, but also mostly right.
Tom Chivers does an excellent job of giving us some historical background, then dives into two key aspects of the use of statistics. These are in science, where the standard approach is frequentist and Bayes only creeps into a few specific applications, such as the accuracy of medical tests, and in decision theory where Bayes is dominant.
If this all sounds very dry and unexciting, it's quite the reverse. I admit, I love probability and statistics, and I am something of a closet Bayesian*), but Chivers' light and entertaining style means that what could have been the mathematical equivalent of debating angels on the heads of a pin becomes both enthralling and relatively easy to understand. You may have to re-read a few sentences, because there is a bit of a head-scrambling concept at the heart of the debate - but it's well worth it.
A trivial way of representing the difference between Bayesian and frequentist statistics is how you respond to the question 'What's the chance of the result being a head?' when looking at a coin that has already been tossed, but that you haven't seen. Bayesian statistics takes into account what you already know. As you don't know what the outcome is, you can only realistically say it's 50:50, or 0.5 in the usual mathematical representation. By contrast, frequentist statistics says that as the coin has been tossed, it is definitely heads or tails with probability 1... but we can't say which. This seems perhaps unimportant - but the distinction becomes crucial when considering the outcome of scientific studies.
Thankfully, Chivers goes into in significant detail the problem that arises because in most scientific use of (frequentist) probability, what the results show is not what we actually want to know. In the social sciences, a marker for a result being 'significant' is a p-value of less that 0.05. This means that if the null hypothesis is true (the effect you are considering doesn't exist), then you would only get this result 1 in 20 times or less. But what we really want to know is not the chance of this result if the hypothesis is true, but rather what's the chance that the hypothesis is true - and that's a totally different thing.
Chivers gives the example of 'it's the difference between "There's only a 1 in 8 billion chance that a given human is the Pope" and "There's only a 1 in 8 billion chance that the Pope is human"'. At risk of repetition because it's so important, frequentist statistics, as used by most scientists, tells us the chance of getting the result if the hypothesis is true; Bayesian statistics works out what the chance is of the hypothesis being true - which most would say is what we really want to know. In fact, as Chivers points out, most scientists don't even know that they aren't showing the chance of the hypothesis being true - and this even true of many textbooks for scientists on how to use statistics.
At this point, most normal humans would say 'Why don't those stupid scientists use Bayes?' But there is a catch. To be able to find how likely the hypothesis is, we need a 'prior probability' - a starting point which Bayes' theorem then modifies using the evidence we have. This feels subjective, and for the first attempt at a study it certainly can be. But, as Chivers points out, in many scientific studies there is existing evidence to provide that starting point - the frequentist approach throws away this useful knowledge.
Is the book perfect? Well, I suspect as a goodish Bayesian I can never say something is perfect. I found it hard to engage with an overlong chapter called 'the Bayesian brain' that is not about using Bayes, but rather trying to show that our brains take this approach, which all felt a bit too hypothetical for me. And Chivers repeats the oft-seen attack on poor old Fred Hoyle, taking his comment about evolution and 'a whirlwind passing through a junkyard creating a Boeing 747' in a way that oversimplifies Hoyle's original meaning. But these are trivial concerns.
I can't remember when I last enjoyed a popular maths book so much. It's a delight.
Tom Chivers does an excellent job of giving us some historical background, then dives into two key aspects of the use of statistics. These are in science, where the standard approach is frequentist and Bayes only creeps into a few specific applications, such as the accuracy of medical tests, and in decision theory where Bayes is dominant.
If this all sounds very dry and unexciting, it's quite the reverse. I admit, I love probability and statistics, and I am something of a closet Bayesian*), but Chivers' light and entertaining style means that what could have been the mathematical equivalent of debating angels on the heads of a pin becomes both enthralling and relatively easy to understand. You may have to re-read a few sentences, because there is a bit of a head-scrambling concept at the heart of the debate - but it's well worth it.
A trivial way of representing the difference between Bayesian and frequentist statistics is how you respond to the question 'What's the chance of the result being a head?' when looking at a coin that has already been tossed, but that you haven't seen. Bayesian statistics takes into account what you already know. As you don't know what the outcome is, you can only realistically say it's 50:50, or 0.5 in the usual mathematical representation. By contrast, frequentist statistics says that as the coin has been tossed, it is definitely heads or tails with probability 1... but we can't say which. This seems perhaps unimportant - but the distinction becomes crucial when considering the outcome of scientific studies.
Thankfully, Chivers goes into in significant detail the problem that arises because in most scientific use of (frequentist) probability, what the results show is not what we actually want to know. In the social sciences, a marker for a result being 'significant' is a p-value of less that 0.05. This means that if the null hypothesis is true (the effect you are considering doesn't exist), then you would only get this result 1 in 20 times or less. But what we really want to know is not the chance of this result if the hypothesis is true, but rather what's the chance that the hypothesis is true - and that's a totally different thing.
Chivers gives the example of 'it's the difference between "There's only a 1 in 8 billion chance that a given human is the Pope" and "There's only a 1 in 8 billion chance that the Pope is human"'. At risk of repetition because it's so important, frequentist statistics, as used by most scientists, tells us the chance of getting the result if the hypothesis is true; Bayesian statistics works out what the chance is of the hypothesis being true - which most would say is what we really want to know. In fact, as Chivers points out, most scientists don't even know that they aren't showing the chance of the hypothesis being true - and this even true of many textbooks for scientists on how to use statistics.
At this point, most normal humans would say 'Why don't those stupid scientists use Bayes?' But there is a catch. To be able to find how likely the hypothesis is, we need a 'prior probability' - a starting point which Bayes' theorem then modifies using the evidence we have. This feels subjective, and for the first attempt at a study it certainly can be. But, as Chivers points out, in many scientific studies there is existing evidence to provide that starting point - the frequentist approach throws away this useful knowledge.
Is the book perfect? Well, I suspect as a goodish Bayesian I can never say something is perfect. I found it hard to engage with an overlong chapter called 'the Bayesian brain' that is not about using Bayes, but rather trying to show that our brains take this approach, which all felt a bit too hypothetical for me. And Chivers repeats the oft-seen attack on poor old Fred Hoyle, taking his comment about evolution and 'a whirlwind passing through a junkyard creating a Boeing 747' in a way that oversimplifies Hoyle's original meaning. But these are trivial concerns.
I can't remember when I last enjoyed a popular maths book so much. It's a delight.
June 16, 2024
I strongly recommend this book. It is an accessible and engaging tour of Bayesian probability theory. The book balances conceptual exposition, breezy intellectual history, and practical applications. The meat of the work concerns two domains ripe for a Bayes' revolution: research science and real-world decision-making/discourse. There is also a special coda about how the brain itself may be a Bayesian agent.
My full review is at Substack:
https://open.substack.com/pub/stetson...
My full review is at Substack:
https://open.substack.com/pub/stetson...
July 25, 2024
Chivers gives a readable description and backstory of statistics along with the feud of Frequentists and Bayesians. He does a great job covering reproducibility issues in scientific research and how “objective” frequentist methods are misused and shows despite being “subjective” how Bayesian framework can provide better use of data. There are many examples with stories of Bayes and major figures like Gauss, Fermat, Fisher, Pearson, etc. Towards the end Chivers gets into how our brains run like prediction machines with bayesian inferences. He helped me see how my mental models are mostly broken in interpreting statistical results. His false positive examples from medical testing are striking. A bit challenging in parts but were great help to update my priors.
June 12, 2024
Fortunately when I saw Tom Chivers’ Everything Is Predictable on the shelf at the bookstore its full cover, rather than just its spine, was facing out. Otherwise I wouldn’t have seen the reference to Bayesian statistics and I probably would not have picked it up. The reason that reference all but forced me to read the book is not because I’m some super user of the Bayesian methodology, at least not consciously. My reason is less intellectual, more emotional. When I was in college I had a favorite professor, Brother Jack D., who made every class interesting, amusing, and informative, so much so that I took six classes with him. The sixth of those classes was a new offering at the time, a class Brother developed himself and lobbied the department to adopt; he enthusiastically described it as a new wave in statistics which was going to have a profound impact on many fields. That class was Bayesian statistics. I wish I could say I immediately recognized the equation on the front of Chivers’ book as the Bayesian theorem, but I took that class in the very early 1980s, so any memory traces furrowed out by my Bayesian studies have long since eroded away.
When I began reading Chivers’ book I was surprised to re-learn that Thomas Bayes developed his theorem back in the eighteenth century. The reality my mind had created in the intervening decades was that Brother had researched a newly developed branch of statistics and fought to bring it to the fore. Not so. The theorem was a couple hundred years old. Had Brother duped me? Fortunately I read on through the Chivers book and learned that Bayes theorem had fallen by the statistical wayside for quite a long time, and not too long before I took Brother’s class it had just started to make a comeback. I was glad not only to preserve my hero’s reputation but also to feel at least a glimmer of recognition as I read my way through the math.
What I didn’t expect was to veer off into topics like the Bayesian aspects of optical illusions, AI, classical conditioning, tennis, schizophrenia, and evolution, all of which I found very interesting and eye opening. Chivers lets me conclude Brother was right to be so enthused.
One last thing before I go. I know it sounds strange to refer to “Brother.” Force of habit; Brother used to tell me, almost begged me, to call him “Jack.” But it just didn’t feel respectful enough, and I still can’t bring myself to do it. So “Brother” it is and always will be, and I felt privileged to read this book as a tribute to him.
When I began reading Chivers’ book I was surprised to re-learn that Thomas Bayes developed his theorem back in the eighteenth century. The reality my mind had created in the intervening decades was that Brother had researched a newly developed branch of statistics and fought to bring it to the fore. Not so. The theorem was a couple hundred years old. Had Brother duped me? Fortunately I read on through the Chivers book and learned that Bayes theorem had fallen by the statistical wayside for quite a long time, and not too long before I took Brother’s class it had just started to make a comeback. I was glad not only to preserve my hero’s reputation but also to feel at least a glimmer of recognition as I read my way through the math.
What I didn’t expect was to veer off into topics like the Bayesian aspects of optical illusions, AI, classical conditioning, tennis, schizophrenia, and evolution, all of which I found very interesting and eye opening. Chivers lets me conclude Brother was right to be so enthused.
One last thing before I go. I know it sounds strange to refer to “Brother.” Force of habit; Brother used to tell me, almost begged me, to call him “Jack.” But it just didn’t feel respectful enough, and I still can’t bring myself to do it. So “Brother” it is and always will be, and I felt privileged to read this book as a tribute to him.
August 14, 2024
The book is mostly repetitive if you already have a good PRIOR knowledge of the topic.
May 29, 2024
This is a great book with a simple message: Thinking Bayesian has many advantages and is how our brain naturally operates. If you’re unfamiliar with probability or statistics, Bayesianism can be summarized as: you have a prior belief about the world (your “prior probability”), you gather evidence (your “likelihood”), and use the two together to get your updated belief (“posterior probability”), which is obtained by multiplying your prior and likelihood together. Your posterior then becomes your new prior, and you repeat the process.
Chivers makes endlessly great points about how this process of incorporating prior probabilities has advantages that conventional “frequentism” doesn’t. Most importantly, a Bayesian approach allows us to answer the question, what is the probability that my hypothesis H is true given the data D?, i.e., P(H|D), whereas frequentism—specifically, a p-value—answers the question, what is the probability that the data D at least as extreme as what I observed could have arisen given the null hypothesis H is true?, i.e., P(D|H).
The latter is by far the more practiced method used by scientists and statisticians, whereas Bayesian approaches are in the minority (though accepted and not unusual nowadays). Chivers rightfully points out that p-values are frequently misunderstood and don’t actually answer the question we often really want to know, i.e., P(H|D). Instead, frequentist approaches indirectly answer this question through replication, meta-analysis, and failed falsification. Bayesianism, you could say, does meta-analysis in a baked-in way—the prior tries to incorporate all past evidence into its approach, then update it based on the newest evidence.
The final two chapters were fascinating in looking at the many examples of implicit Bayesianism in the world and the process by which the brain operates in accommodating new information to update beliefs. Regarding the former (Bayesianism in the world), many cognitive biases discovered by Kahneman & Tversky and others could be described as deviations from Bayesian logic, such as the conjunction fallacy and framing effects, or medical decision-making, whereby medical professionals fail to incorporate base rates into their diagnostic assessments. As an example of the latter (Bayesianism in the brain), in individuals with schizophrenia, their priors are notably weaker, meaning their predictions about sensory data are less accurate and less constrained by previous sensory input—which led to the accurate prediction that schizophrenic individuals are less susceptible to certain optical illusions.
I have one major substantive criticism: Chivers explains frequentism as though it’s all about binary decision-making via p-values, while ignoring confidence intervals, effect size estimates, and other metrics that quantify model performance (R^2, AIC/BIC, etc.). Though Chivers at one point says “We’ll talk more about p-values and confidence intervals a bit later”, there really isn’t much more mention of confidence intervals throughout the whole book (he must’ve forgotten that he left this sentence in the book). Undoubtedly, he must know that sole reliance on p-values is a terrible idea even if one interprets them accurately. Now, it’s true that frequentism generally cannot directly allow us to compute the probability that a hypothesis is true given the data, but there are many other goals with statistical analysis that Chivers only vaguely alludes to throughout the book.
Notwithstanding my gripes, this was a truly wonderfully written and insightful book that I learned a lot from. Highly recommended.
Chivers makes endlessly great points about how this process of incorporating prior probabilities has advantages that conventional “frequentism” doesn’t. Most importantly, a Bayesian approach allows us to answer the question, what is the probability that my hypothesis H is true given the data D?, i.e., P(H|D), whereas frequentism—specifically, a p-value—answers the question, what is the probability that the data D at least as extreme as what I observed could have arisen given the null hypothesis H is true?, i.e., P(D|H).
The latter is by far the more practiced method used by scientists and statisticians, whereas Bayesian approaches are in the minority (though accepted and not unusual nowadays). Chivers rightfully points out that p-values are frequently misunderstood and don’t actually answer the question we often really want to know, i.e., P(H|D). Instead, frequentist approaches indirectly answer this question through replication, meta-analysis, and failed falsification. Bayesianism, you could say, does meta-analysis in a baked-in way—the prior tries to incorporate all past evidence into its approach, then update it based on the newest evidence.
The final two chapters were fascinating in looking at the many examples of implicit Bayesianism in the world and the process by which the brain operates in accommodating new information to update beliefs. Regarding the former (Bayesianism in the world), many cognitive biases discovered by Kahneman & Tversky and others could be described as deviations from Bayesian logic, such as the conjunction fallacy and framing effects, or medical decision-making, whereby medical professionals fail to incorporate base rates into their diagnostic assessments. As an example of the latter (Bayesianism in the brain), in individuals with schizophrenia, their priors are notably weaker, meaning their predictions about sensory data are less accurate and less constrained by previous sensory input—which led to the accurate prediction that schizophrenic individuals are less susceptible to certain optical illusions.
I have one major substantive criticism: Chivers explains frequentism as though it’s all about binary decision-making via p-values, while ignoring confidence intervals, effect size estimates, and other metrics that quantify model performance (R^2, AIC/BIC, etc.). Though Chivers at one point says “We’ll talk more about p-values and confidence intervals a bit later”, there really isn’t much more mention of confidence intervals throughout the whole book (he must’ve forgotten that he left this sentence in the book). Undoubtedly, he must know that sole reliance on p-values is a terrible idea even if one interprets them accurately. Now, it’s true that frequentism generally cannot directly allow us to compute the probability that a hypothesis is true given the data, but there are many other goals with statistical analysis that Chivers only vaguely alludes to throughout the book.
Notwithstanding my gripes, this was a truly wonderfully written and insightful book that I learned a lot from. Highly recommended.
August 20, 2024
A very entertaining and light introduction to Bayesian statistics that requires no background knowledge.
Stuffed with examples and historical anecdotes, Chivers wrote a very accessible and fun book that I would recommend to anyone with the slightest interest in science. At the end the book could have been a few chapters shorter and I think it would have actually profited from adding more equations and explaining the underlying math in more detail. Still, I really liked the authors style and I’m looking forward to reading more of his work.
Stuffed with examples and historical anecdotes, Chivers wrote a very accessible and fun book that I would recommend to anyone with the slightest interest in science. At the end the book could have been a few chapters shorter and I think it would have actually profited from adding more equations and explaining the underlying math in more detail. Still, I really liked the authors style and I’m looking forward to reading more of his work.
July 19, 2024
An accessible, interesting and at times humourous introduction to Bayesian reasoning and it's myriad applications in science, psychology, daily life etc. It's one of those concepts that you can apply to almost anything and look at it through that lens. But don't worry about it completely warping your worldview: if your brain's intstinctually Bayesian circuits for belief-updating are well calibrated, this book will just add a healthy few per-cent of Baysian flavour to your outlook.
May 10, 2024
This book is an overview of Bayes theory, a history of Bayes theory, and many examples of how to use Bayesian Statistics. It does this all while being conscious of the fact that many people are confused by Bayes, misunderstand Bayes, and either undervalue or overvalue the relevancy of Bayes to modern life.
I recently read A Brief History of Intelligence, and Chivers here manages to connect the understanding of Bayesian inference to the brain structures and neurochemical processes that Max Bennett talks about in his history, though I do not know that either author is aware of the other (there is no mention in the index). I mention this as it adds credence to his idea that our consciousness is indeed Bayesian in essential ways.
Also his discussion of the work of Aubrey Clayton who wrote Bernoulli's Fallacy was helpful in clarifying some of Clayton's points.
I highly recommend this book, and the podcast the Tom Chivers does called The Studies Show.
I recently read A Brief History of Intelligence, and Chivers here manages to connect the understanding of Bayesian inference to the brain structures and neurochemical processes that Max Bennett talks about in his history, though I do not know that either author is aware of the other (there is no mention in the index). I mention this as it adds credence to his idea that our consciousness is indeed Bayesian in essential ways.
Also his discussion of the work of Aubrey Clayton who wrote Bernoulli's Fallacy was helpful in clarifying some of Clayton's points.
I highly recommend this book, and the podcast the Tom Chivers does called The Studies Show.
September 8, 2024
Once upon a time in the land of Certaintia, there lived a wise old scholar named Bayes, whose insights had changed the way the people viewed their world. No longer was life a chaotic mess of uncertainty. Bayes had taught them that with patience, observation, and a careful process of updating their beliefs, even the most unpredictable events could be understood. The farmers, fishermen, and even the king himself had grown prosperous thanks to his remarkable theorem.
But not everyone in Certaintia was convinced.
Among the crowds of grateful villagers and curious scholars, there were some skeptics. These critics, led by a sharp-tongued philosopher named Determinax, scoffed at Bayes' ideas. “This so-called ‘theorem’ of yours relies too much on prior beliefs, old man,” Determinax declared. “What if your initial beliefs are wrong? What if you’re foolish enough to place trust in false evidence? Your whole system will collapse like a house of cards!”
The people of Certaintia began to murmur. Could Determinax be right? What if they were using Bayes’ method but starting from the wrong assumptions? What if they were led astray by faulty evidence?
Undeterred, Bayes calmly rose to address his critics. "My dear Determinax, you raise important concerns," he began, his voice steady and kind. “Indeed, if you start with a poor belief or rely on bad evidence, your predictions will falter. But that is the beauty of my method — it allows for learning and correction over time."
The crowd leaned in, eager to hear more. Bayes continued, “You see, my critics argue that starting with the wrong belief will lead you astray, but in truth, the world constantly provides us with new information. As we gather more evidence, our prior beliefs matter less, and the truth becomes clearer. Imagine a farmer who once believed rain never comes in spring. After several wet springs, the farmer adjusts his belief — and the more springs he experiences, the more accurate his predictions become.”
Determinax wasn’t convinced. “But what about when evidence is scarce? What if the clues the world gives us are faint and unreliable?”
Bayes smiled. “Ah, but that is where probability becomes our guide. Even when evidence is scarce, we can express our uncertainty in precise terms. We can say, ‘We are not sure, but this seems more likely than that.’ My theorem does not promise absolute certainty; it promises a way to measure and handle uncertainty with care. And as new evidence trickles in, no matter how small, we refine our beliefs.”
Another voice rose from the crowd, this time from an old merchant. “But what if we refuse to let go of our old beliefs? What if someone clings stubbornly to false ideas, no matter the evidence?”
Bayes nodded thoughtfully. “Indeed, stubbornness can be our greatest enemy. Some people hold on too tightly to their priors, ignoring the evidence in front of them. But this is not the fault of the theorem — it is the fault of the believer. Those who refuse to update their beliefs are no different than a ship that ignores the stars and crashes upon the rocks. My theorem works best when used with an open mind and a willingness to learn.”
The crowd murmured in approval, and even Determinax seemed to soften. Bayes’ wisdom was not about knowing everything from the start, but about a commitment to continuously improve one’s understanding.
Yet, Determinax had one last objection. “But Bayes, what about when you cannot gather enough evidence? In cases where the unknown looms large, doesn’t your system fail?”
Bayes shook his head gently. “In such cases, my dear Determinax, my system reminds us that it is okay not to know. When evidence is scarce, we can still estimate our uncertainty and proceed with caution, always aware that more information may change our course. Unlike those who claim absolute certainty in ignorance, we remain humble, ever open to learning more.”
At last, Determinax fell silent, pondering the wise scholar’s words. He could not deny that Bayes’ method encouraged not just prediction, but humility — a way of acknowledging that one’s knowledge was always incomplete and subject to change.
The people of Certaintia, having heard the debate, stood firm in their faith in Bayes’ theorem, but now they understood it better. They saw that Bayes did not promise perfection, but a way to navigate uncertainty with grace. His critics had challenged him, but instead of faltering, Bayes had shown that his method was not rigid, but flexible — a tool for those willing to embrace the complexity of the world.
And so, Certaintia continued to thrive, as its people, guided by Bayes’ wisdom, learned not only to predict the future but to adapt and grow wiser with each passing day. Even Determinax, once a fierce critic, began to use the theorem in his own work, discovering that the world, though uncertain, was always revealing new secrets to those willing to listen.
And they all lived wisely — if not always predictably — ever after.
But not everyone in Certaintia was convinced.
Among the crowds of grateful villagers and curious scholars, there were some skeptics. These critics, led by a sharp-tongued philosopher named Determinax, scoffed at Bayes' ideas. “This so-called ‘theorem’ of yours relies too much on prior beliefs, old man,” Determinax declared. “What if your initial beliefs are wrong? What if you’re foolish enough to place trust in false evidence? Your whole system will collapse like a house of cards!”
The people of Certaintia began to murmur. Could Determinax be right? What if they were using Bayes’ method but starting from the wrong assumptions? What if they were led astray by faulty evidence?
Undeterred, Bayes calmly rose to address his critics. "My dear Determinax, you raise important concerns," he began, his voice steady and kind. “Indeed, if you start with a poor belief or rely on bad evidence, your predictions will falter. But that is the beauty of my method — it allows for learning and correction over time."
The crowd leaned in, eager to hear more. Bayes continued, “You see, my critics argue that starting with the wrong belief will lead you astray, but in truth, the world constantly provides us with new information. As we gather more evidence, our prior beliefs matter less, and the truth becomes clearer. Imagine a farmer who once believed rain never comes in spring. After several wet springs, the farmer adjusts his belief — and the more springs he experiences, the more accurate his predictions become.”
Determinax wasn’t convinced. “But what about when evidence is scarce? What if the clues the world gives us are faint and unreliable?”
Bayes smiled. “Ah, but that is where probability becomes our guide. Even when evidence is scarce, we can express our uncertainty in precise terms. We can say, ‘We are not sure, but this seems more likely than that.’ My theorem does not promise absolute certainty; it promises a way to measure and handle uncertainty with care. And as new evidence trickles in, no matter how small, we refine our beliefs.”
Another voice rose from the crowd, this time from an old merchant. “But what if we refuse to let go of our old beliefs? What if someone clings stubbornly to false ideas, no matter the evidence?”
Bayes nodded thoughtfully. “Indeed, stubbornness can be our greatest enemy. Some people hold on too tightly to their priors, ignoring the evidence in front of them. But this is not the fault of the theorem — it is the fault of the believer. Those who refuse to update their beliefs are no different than a ship that ignores the stars and crashes upon the rocks. My theorem works best when used with an open mind and a willingness to learn.”
The crowd murmured in approval, and even Determinax seemed to soften. Bayes’ wisdom was not about knowing everything from the start, but about a commitment to continuously improve one’s understanding.
Yet, Determinax had one last objection. “But Bayes, what about when you cannot gather enough evidence? In cases where the unknown looms large, doesn’t your system fail?”
Bayes shook his head gently. “In such cases, my dear Determinax, my system reminds us that it is okay not to know. When evidence is scarce, we can still estimate our uncertainty and proceed with caution, always aware that more information may change our course. Unlike those who claim absolute certainty in ignorance, we remain humble, ever open to learning more.”
At last, Determinax fell silent, pondering the wise scholar’s words. He could not deny that Bayes’ method encouraged not just prediction, but humility — a way of acknowledging that one’s knowledge was always incomplete and subject to change.
The people of Certaintia, having heard the debate, stood firm in their faith in Bayes’ theorem, but now they understood it better. They saw that Bayes did not promise perfection, but a way to navigate uncertainty with grace. His critics had challenged him, but instead of faltering, Bayes had shown that his method was not rigid, but flexible — a tool for those willing to embrace the complexity of the world.
And so, Certaintia continued to thrive, as its people, guided by Bayes’ wisdom, learned not only to predict the future but to adapt and grow wiser with each passing day. Even Determinax, once a fierce critic, began to use the theorem in his own work, discovering that the world, though uncertain, was always revealing new secrets to those willing to listen.
And they all lived wisely — if not always predictably — ever after.
May 30, 2024
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:
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:
May 13, 2024
Thanks to the publisher and Netgalley for this eARC.
In “Everything Is Predictable: How Bayesian Statistics Explain Our World,” Tom Chivers offers a compelling journey through the lens of Bayes’s theorem, a cornerstone of rational thought and a powerful tool for making sense of uncertainty. Chivers, an acclaimed science writer, presents a user-friendly exploration of a mathematical concept that, while seemingly esoteric, underpins much of our decision-making process in the modern world.
The book is structured around the theorem’s simple yet profound premise: the probability of an event is determined not just by the evidence at hand but also by our prior beliefs and knowledge. Chivers masterfully illustrates this through a variety of real-world applications, from medical diagnostics to legal judgments, showcasing the theorem’s versatility and its potential to lead to both triumphs and missteps when misunderstood or misapplied.
What sets this work apart is Chivers’s ability to fuse biography, history, and technical explanation into a narrative that is as educational as it is entertaining. Readers are treated to a biography of Thomas Bayes, the 18th-century Presbyterian minister and mathematician, whose work has found relevance in fields as diverse as artificial intelligence and epidemiology. The historical context enriches the reader’s understanding of the theorem’s development and its pivotal role in the evolution of statistics.
Chivers’s writing is accessible and engaging, with a wit that enlivens the subject matter. He navigates complex statistical concepts with ease, ensuring that readers, regardless of their mathematical background, can grasp the significance of Bayesian thinking. The book is not just an introduction to a mathematical theory but an invitation to view the world through a Bayesian lens, recognizing patterns and probabilities in the chaos of everyday life.
“Everything Is Predictable” is a testament to the power of a single idea to reshape our understanding of the world. It is a must-read for anyone interested in the intersection of mathematics, philosophy, and the pursuit of knowledge. Chivers has not only written an ingenious introduction to Bayesian statistics but has also provided readers with a new framework for considering the predictability of the unpredictable.
In “Everything Is Predictable: How Bayesian Statistics Explain Our World,” Tom Chivers offers a compelling journey through the lens of Bayes’s theorem, a cornerstone of rational thought and a powerful tool for making sense of uncertainty. Chivers, an acclaimed science writer, presents a user-friendly exploration of a mathematical concept that, while seemingly esoteric, underpins much of our decision-making process in the modern world.
The book is structured around the theorem’s simple yet profound premise: the probability of an event is determined not just by the evidence at hand but also by our prior beliefs and knowledge. Chivers masterfully illustrates this through a variety of real-world applications, from medical diagnostics to legal judgments, showcasing the theorem’s versatility and its potential to lead to both triumphs and missteps when misunderstood or misapplied.
What sets this work apart is Chivers’s ability to fuse biography, history, and technical explanation into a narrative that is as educational as it is entertaining. Readers are treated to a biography of Thomas Bayes, the 18th-century Presbyterian minister and mathematician, whose work has found relevance in fields as diverse as artificial intelligence and epidemiology. The historical context enriches the reader’s understanding of the theorem’s development and its pivotal role in the evolution of statistics.
Chivers’s writing is accessible and engaging, with a wit that enlivens the subject matter. He navigates complex statistical concepts with ease, ensuring that readers, regardless of their mathematical background, can grasp the significance of Bayesian thinking. The book is not just an introduction to a mathematical theory but an invitation to view the world through a Bayesian lens, recognizing patterns and probabilities in the chaos of everyday life.
“Everything Is Predictable” is a testament to the power of a single idea to reshape our understanding of the world. It is a must-read for anyone interested in the intersection of mathematics, philosophy, and the pursuit of knowledge. Chivers has not only written an ingenious introduction to Bayesian statistics but has also provided readers with a new framework for considering the predictability of the unpredictable.
May 24, 2024
A short history of probabilistic thought and statistics and a longer discussion of how Bayesian statistics might help us do science and to make decisions in the world.
My best way of understanding Bayesian statistics is through an example. If you had a test for a disease that was 95% accurate then if you had the disease, you’d have a 95% chance of getting a positive test and if you didn’t have the disease you’d have a 95% chance of a negative test. This is a frequentist claim often used to test for significance in science. Bayes theorem can be used to ask the more useful question – do I have the disease? To answer it you also need some prior estimate of the probability, in this case the prevalence of the disease in the population (say 1%). If there are 1,000,000 people in your population, 10,000 would have the disease and 990,000 would not. If all the positive people took the test, then 9,500 would test positive and 500 negatives. If all the negative people took the test, then 49,500 of them would test positive and 940,500 negative. If you took a test and it was positive the chance you have the disease is 9,500/ (9,500 +49,500), about 16%. The 16% is probably more useful to you than the 95% accuracy of the test and you can only calculate it with some prior knowledge of the prevalence of the disease in the population.
Bayesian statistics, according to this book, provides a natural and useful way to think about the world. New information can only serve to shift your existing understanding, your priors, and not answer the question by itself. The author explains this is how practical decision-making works and why science might be more or less convincing to different people (with different priors).
My criticisms are that it's a little repetitive and sometimes stretches to incorporate Bayes into everything but on the whole entertaining and informative. The author's asides and comments on the narrative are charming.
My best way of understanding Bayesian statistics is through an example. If you had a test for a disease that was 95% accurate then if you had the disease, you’d have a 95% chance of getting a positive test and if you didn’t have the disease you’d have a 95% chance of a negative test. This is a frequentist claim often used to test for significance in science. Bayes theorem can be used to ask the more useful question – do I have the disease? To answer it you also need some prior estimate of the probability, in this case the prevalence of the disease in the population (say 1%). If there are 1,000,000 people in your population, 10,000 would have the disease and 990,000 would not. If all the positive people took the test, then 9,500 would test positive and 500 negatives. If all the negative people took the test, then 49,500 of them would test positive and 940,500 negative. If you took a test and it was positive the chance you have the disease is 9,500/ (9,500 +49,500), about 16%. The 16% is probably more useful to you than the 95% accuracy of the test and you can only calculate it with some prior knowledge of the prevalence of the disease in the population.
Bayesian statistics, according to this book, provides a natural and useful way to think about the world. New information can only serve to shift your existing understanding, your priors, and not answer the question by itself. The author explains this is how practical decision-making works and why science might be more or less convincing to different people (with different priors).
My criticisms are that it's a little repetitive and sometimes stretches to incorporate Bayes into everything but on the whole entertaining and informative. The author's asides and comments on the narrative are charming.
June 26, 2024
The book is great, and the author, Tom Chivers is a great writer which kept me entertained in every page.
So why a 4/5?
As a bayesian statistician myself, I personally felt that Chivers abused the terminology of Bayes Theorem quite too much. Certainly this book was written for the general audience, but I felt that he didn't used some terminology accordingly.
I am speaking of the Posterior Distribution. I felt that he used posterior distribution and Bayes Theorem interchangeably, which if you read a textbook of Bayes Statistics like "Bayesian Data Analysis, by Andrew Gelman, et al." they mentioned that Bayesian theorem and posterior distribution are two different things. (Yes, you need to use Bayes Theorem to prove the posterior distribution.)
Nevertheless, I felt that this book is a way to explain a non mathematician what Bayesian statistics does, but is not a textbook, meaning that really doing Bayesian statistics isn't as easy as it sounds.
One thing that I didn't recall Chivers mentioned is that Frequentist statistics is significantly, much much, easier to work with. Not just in terms of the computational power that you need, but even if you decide to work by hand, Bayesian Statistics requires a you to do a lot of integrations, beyond finding the moments of your distributions.
Anyhow, I would like for more universities to teach Bayesian statistics as a core module.
(Pardon me for any inconvenience in this text, I only had my phone when writing this review.)
So why a 4/5?
As a bayesian statistician myself, I personally felt that Chivers abused the terminology of Bayes Theorem quite too much. Certainly this book was written for the general audience, but I felt that he didn't used some terminology accordingly.
I am speaking of the Posterior Distribution. I felt that he used posterior distribution and Bayes Theorem interchangeably, which if you read a textbook of Bayes Statistics like "Bayesian Data Analysis, by Andrew Gelman, et al." they mentioned that Bayesian theorem and posterior distribution are two different things. (Yes, you need to use Bayes Theorem to prove the posterior distribution.)
Nevertheless, I felt that this book is a way to explain a non mathematician what Bayesian statistics does, but is not a textbook, meaning that really doing Bayesian statistics isn't as easy as it sounds.
One thing that I didn't recall Chivers mentioned is that Frequentist statistics is significantly, much much, easier to work with. Not just in terms of the computational power that you need, but even if you decide to work by hand, Bayesian Statistics requires a you to do a lot of integrations, beyond finding the moments of your distributions.
Anyhow, I would like for more universities to teach Bayesian statistics as a core module.
(Pardon me for any inconvenience in this text, I only had my phone when writing this review.)
July 13, 2024
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 regarding OJ is pretty interesting as well.
Popular answers are 75% or 90%. The correct answer is about 8%. If you are not interested in why it's 8% then there is no reason to read the book or the remainder of my review. I get it, not everyone enjoys math, and for that I blame the education system.
Bayes theorem is all about using your prior beliefs or just “prior” as it's used today, to influence your decision making. We all do it every day. The older we become, our priors become stronger. This is called wisdom, and its an advantage until the world changes, then we have a hard time changing our beliefs.
The book admits that for every formula printed, the profit will be cut in ½. So the author only has one formula. Unfortunately he compensates for the lack of mathematical crispness with boat load of words. There were just so many examples that were variations on a theme.
My high level synopsis of Bayes theorem is one of my favorite quotes. “The best predictor of future behavior is past behavior”.
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 regarding OJ is pretty interesting as well.
Popular answers are 75% or 90%. The correct answer is about 8%. If you are not interested in why it's 8% then there is no reason to read the book or the remainder of my review. I get it, not everyone enjoys math, and for that I blame the education system.
Bayes theorem is all about using your prior beliefs or just “prior” as it's used today, to influence your decision making. We all do it every day. The older we become, our priors become stronger. This is called wisdom, and its an advantage until the world changes, then we have a hard time changing our beliefs.
The book admits that for every formula printed, the profit will be cut in ½. So the author only has one formula. Unfortunately he compensates for the lack of mathematical crispness with boat load of words. There were just so many examples that were variations on a theme.
My high level synopsis of Bayes theorem is one of my favorite quotes. “The best predictor of future behavior is past behavior”.
September 19, 2024
Easy five stars. I’m all-in on Bayesian statistics.
There are drawbacks — it’s tough to select the right priors, it can be harder to compute results, and it is difficult to implement in large organizations — but I buy Chivers’ claim that it is fundamentally consistent with how we make decisions as humans. We have prior beliefs, we come across new data, and we update our beliefs based on the strength of our priors and the amount of signal from this new data.
Are our priors subjective? Of course, and they will never be perfectly correct, but Chivers makes the case that this is often still better than not including anything. In other words, Frequentist statistics does not actually provide the objectivity we seek. It can lead to arbitrary decision boundaries (p=0.05) and a bias towards implausible hypotheses, some of which we’ve seen play out with the replication crisis.
I loved “Bernoulli’s Fallacy” and there was definitely some overlap but I found this one to be less dogmatic and more balanced. Chivers explains why Frequentist statistics gained ground and some of its advantages, but by the end, it’s clear where he lands.
I would love to learn more about the specifics of Bayesian statistics now but I found this book to be highly readable and a great introduction for those new to the field.
There are drawbacks — it’s tough to select the right priors, it can be harder to compute results, and it is difficult to implement in large organizations — but I buy Chivers’ claim that it is fundamentally consistent with how we make decisions as humans. We have prior beliefs, we come across new data, and we update our beliefs based on the strength of our priors and the amount of signal from this new data.
Are our priors subjective? Of course, and they will never be perfectly correct, but Chivers makes the case that this is often still better than not including anything. In other words, Frequentist statistics does not actually provide the objectivity we seek. It can lead to arbitrary decision boundaries (p=0.05) and a bias towards implausible hypotheses, some of which we’ve seen play out with the replication crisis.
I loved “Bernoulli’s Fallacy” and there was definitely some overlap but I found this one to be less dogmatic and more balanced. Chivers explains why Frequentist statistics gained ground and some of its advantages, but by the end, it’s clear where he lands.
I would love to learn more about the specifics of Bayesian statistics now but I found this book to be highly readable and a great introduction for those new to the field.
June 19, 2024
This is a worthwhile introduction to Bayes, although the book goes rather far afield in it second half, to the point that anything to takes into account previous information is presumed to be Bayesian. I think someone needed to provide the author a Venn diagram to show how Bayes is merely a subset of rational thinking, not nearly the whole shebang.
Another odd thing is that he introduces Bayes' theorem very early on, but then hardly references it again! Sure, he more or less applies it to various insights in statistics, but he stays away from the mechanics of Bayes' equation and why it works.
I will say that the author did a great job of showing many important applications of Bayes' thought, such as in medical testing. People often don't understand how they can take a test that is 99% effective, receive news that the test came back positive (for cancer or whatever), then be told there's only a 3% chance (for example) that they have cancer. It all comes down to base-rates, folks; that is, one's priors. And understanding Bayes will help you understand why.
Go ahead, read this book. Just don't complain that I didn't warn you ahead of time that the first half will be better than the second. I did.
Another odd thing is that he introduces Bayes' theorem very early on, but then hardly references it again! Sure, he more or less applies it to various insights in statistics, but he stays away from the mechanics of Bayes' equation and why it works.
I will say that the author did a great job of showing many important applications of Bayes' thought, such as in medical testing. People often don't understand how they can take a test that is 99% effective, receive news that the test came back positive (for cancer or whatever), then be told there's only a 3% chance (for example) that they have cancer. It all comes down to base-rates, folks; that is, one's priors. And understanding Bayes will help you understand why.
Go ahead, read this book. Just don't complain that I didn't warn you ahead of time that the first half will be better than the second. I did.
July 5, 2024
I'm not sure why, but I've recently seen a lot of mentions of Bayesian statistics in the things I read (esp. the use of the word "priors"): So I decided to read a book about it. There are two sides to this book. One is a critique of "frequentist" statistics (i.e., mainstream statistics that compute a p-value -- this is the statistics you learned in college). That's quite good, and there's an entertaining chapter on how many studies nowadays can't be reproduced, in part because scientists are prowling their data for subsets that support decent p-values); change the data just a bit, and you struggle to find the same likelihoods.
The other side is a kind of "theory of everything" for Bayesian ways of thinking. This actually seems a little less successful -- but I might have to read the book again. In short, the book memorably argues that everything is ultimately prediction. There's a line at the end that says "beliefs are predictions." The author would likely be the first to admit -- on Bayesian grounds -- that anyone who believes that beliefs are not predictions would be entirely unswayed by this book.
The other side is a kind of "theory of everything" for Bayesian ways of thinking. This actually seems a little less successful -- but I might have to read the book again. In short, the book memorably argues that everything is ultimately prediction. There's a line at the end that says "beliefs are predictions." The author would likely be the first to admit -- on Bayesian grounds -- that anyone who believes that beliefs are not predictions would be entirely unswayed by this book.
September 17, 2024
The book starts with a history of Thomas Bayes - I knew about Bayesian Theorem, but didn't know anything about Bayes himself, definitely didn't know that the theorem itself is about 200 years old.
It continues to talk about the differences between Frequentists and Bayesian statisticians and how each of them approach a problem at hand. It was intriguing to realize "what p-value informs you". It was also very insightful to see how the author connects AI, schizophrenia, evolution and inner working of our brain to Bayesian thinking.
"All life is trying to reduce the difference between what they predict and what they experience because the brain hates prediction error and wants to minimize it." - absolutely relatable.
My respect towards Bayes has increased n-fold after reading this book. Credit also to the author to put forth a perplexing subject like Statistics in simple language.
It continues to talk about the differences between Frequentists and Bayesian statisticians and how each of them approach a problem at hand. It was intriguing to realize "what p-value informs you". It was also very insightful to see how the author connects AI, schizophrenia, evolution and inner working of our brain to Bayesian thinking.
"All life is trying to reduce the difference between what they predict and what they experience because the brain hates prediction error and wants to minimize it." - absolutely relatable.
My respect towards Bayes has increased n-fold after reading this book. Credit also to the author to put forth a perplexing subject like Statistics in simple language.
March 9, 2024
Seriously, more people should read books about science for fun. If people tried books like this, they'd understand what they're missing.
Sure, there is math, but this book is really about how predicting things and wanting to be able to predict things is part of everyday life for everyone. Even something ad simple as how we perceive color can depend on what we expect to see.
The book is conversational and hilarious in places, especially when talking about scientists. My favorite might be the group of scientists who made up their own songs about statistics.
Thanks so much to NetGalley for letting me read this
Sure, there is math, but this book is really about how predicting things and wanting to be able to predict things is part of everyday life for everyone. Even something ad simple as how we perceive color can depend on what we expect to see.
The book is conversational and hilarious in places, especially when talking about scientists. My favorite might be the group of scientists who made up their own songs about statistics.
Thanks so much to NetGalley for letting me read this
July 29, 2024
"Everything is Predictable" by Tim Chivers offers a fascinating look into the patterns and systems that shape our world. Chivers combines scientific analysis with engaging storytelling, making complex concepts accessible and relevant. The book's strength lies in its unique perspective and the author's ability to weave facts into a compelling narrative.
While some readers might find the depth and detail overwhelming, Chivers' clear explanations and real-world examples make it an enlightening read. "Everything is Predictable" is a captivating and thought-provoking book, highly recommended for those interested in understanding the predictable nature of our world. I rate it 4 out of 5 stars.
While some readers might find the depth and detail overwhelming, Chivers' clear explanations and real-world examples make it an enlightening read. "Everything is Predictable" is a captivating and thought-provoking book, highly recommended for those interested in understanding the predictable nature of our world. I rate it 4 out of 5 stars.
September 1, 2024
I am a big fan of probability, statistics and bayes. I am a physician. The book is very relevant to my line of work. I am shocked at how little or no explanation is given to actual formula. There are no pictures, ven diagrams to explain what bayes theorem actually is at least in the first few chapters that I have read. This book assumes a very high familiarity with bayes and statistical thinking. It almost feels the author has spent so much time thinking about this work that he has forgotten his audience.This makes reading the book pointless. It is written in a bery dry way. Its a shame be because i agree everything to some extent csn be explained by this theorem.
August 1, 2024
This is probably better for someone that knows very little about statistics or Bayes. Easy to read and very accessible. The last few chapters about AI and the brain were the least interesting to me.
My takeaways:
- I'm going to try to be more explicit in using a Bayesian approach to thinking through problems/questions. Some of that is just common sense but it's easy to get stuck to priors or be too easily swayed with no priors.
- Love the Oliver Cromwell quote, "I beseech you, in the bowels of Christ, think it possible you may be mistaken."
My takeaways:
- I'm going to try to be more explicit in using a Bayesian approach to thinking through problems/questions. Some of that is just common sense but it's easy to get stuck to priors or be too easily swayed with no priors.
- Love the Oliver Cromwell quote, "I beseech you, in the bowels of Christ, think it possible you may be mistaken."
August 7, 2024
Yay! Little did I know that Bayesian statistics is not as popular as I thought. I’ve only been trained in Bayesian stats and thought it completely ruled the world, but didn’t realize the extent of the dominance of frequentist and the debate between the two.
Only rating it 4 because I still don’t fully understand everything, and I believe that’s mostly my fault but also sometimes felt the explanations or repetition of important information lacking. Really great motivation of Bayesian statistics, particularly given his arguments of how the brain and evolution work.
Only rating it 4 because I still don’t fully understand everything, and I believe that’s mostly my fault but also sometimes felt the explanations or repetition of important information lacking. Really great motivation of Bayesian statistics, particularly given his arguments of how the brain and evolution work.
May 7, 2024
I thoroughly enjoyed this book. I found the writing to be conversational and the explanations clear. Chivers made excellent use of analogies. The book could have lapsed into a treatise on math but it didn’t. The book maintained an even pacing, with frequent injections of subject-related humour. I also appreciated all the biographical information. My advance reader copy was provided by the publisher via Netgalley in exchange for an honest review.
September 8, 2024
Genius, genius, genius. I'll admit: I don't think I understood all of it, and will probably need another read to fully grasp the concept. But it was SO FUN to have my brain warped in this way. The author has a lot of respect for his readers and doesn't boil everything down to an overly-simplistic position, but he does speak with clarity and also doesn't overly add complication language just to sound smart, either. Also the topic itself is fascinating and under-reported. Bravo - fantastic book!
June 14, 2024
Best book I read so far in 2024. Made me think of implementing a good understanding of the basics of Bayes for kids as part of a toolbox to deal with polarization and social media use. Looking forward to help spread the marvelous idea by Bayes and have it be the basis for weighing knowledge and understanding epistemology of a new generation.
June 11, 2024
Super fun book and incredibly well explained. The material he covers in the book is dense! And I probably would have been better off reading rather than listening to it. But still, he did a great job explaining some really complicated ideas really well. It's also funny!
July 12, 2024
Very good exposition of living in a probabilistic world. Makes it all seem blindingly obvious.
The only thing I don't like is the book title and tag line. I'd go with:
"Making better decisions in an uncertain world: why and how Bayesian methods make sense"
The only thing I don't like is the book title and tag line. I'd go with:
"Making better decisions in an uncertain world: why and how Bayesian methods make sense"
Want to read
April 18, 2024#GoodreadsGiveaway
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