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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.
378 pages, Kindle Edition
First published April 25, 2024
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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:
My full review is at Substack:
Read
March 12, 2025Imagine you've thrown a coin, caught it but still have not had a chance to look at it. What are the chances it is a head? Think of it for a second before reading further. Here is a choice of the two possible answers: 1) 50:50; 2) 100% or 0 chance: the outcome is already certain; the result of it you do not know yet, but it is already out there. The answer to this question would define if you are inclined to be a Baeysian or not (this "not" is often called "frequentist"). It is not as simple as it sounds as the implications of this could be quite broad, almost on the level of the whole coherent world view. If your answer was 50:50, you are a Bayesian indeed believing that a probability is more subjective than objective (it can be only based upon someone's subjective priors to start with.) In the case of this coin experiment it is still uncertain for you, so it is 50% chance. Though for someone who has already taken a pick it is what it is.
Recently with Covid we dealt with the another example of a bayesian thinking or the lack of it. If you have a covid test with 95% accuracy, and it came back positive. Does it mean the chance you have a Covid is 95%? The correct answer is "no". It is much lower as it also depends on the rate of prevalence in the population at the moment you've tested. There were many arguments at that time related to the incorrect interpretation of statistics. Some of them were pretty grim. For better examples and more explanation how this works I would recommend to read this book. Chivers explains it with the great clarity. I think he is a journalist rather than a scientist or mathematician. So the book is a little sketchy. It covers a lot of ground from the examples like that to the biography of Reverend Bayes. Also he interviews neuroscientists, psychiatrists and psychologists for this book.
The debate between the frequentists and the bayesians is not an empty one. It has a got a pretty fundamental applications for many serious things such as scientific method for example. The statistical experiment of testing hypotheses for the purpose of science is based on frequentist logic. The debate is raging for more than a century already. So far the frequentists prevail but they are losing ground, especially with emergence of an AI and so called replication crisis in science. Many of the hypotheses accepted are not confirmed when an experiment is replicated. The were a few scandals recently, most prominently in social psychology propagating different 'nudge' theories.
The chapter I was personally mostly fascinated with is about a hypothesis of Bayesian brain It is gaining ground between the neuroscientists as far as I understand but its root is more remote in the 19th century":
And nowadays some scientists think it is much broader than just perception. It is all cognition and emotions as well. Around 200 million years ago the mammals have evolved neocortex. This is where it properly starts. But because it is so complicated to summarise i would be really brief: the mammals’s brain produces a full 3d model of the reality. Based upon this model it can simulate different scenarios just in its head and predict future: both its own actions and the possible changes in the environment. Also it identifies the gaps between the model and the sensory input and try to minimise them either by adjusting the model or taking actions to adjust the environment closer to the model. Your imagination is also basically your brain playing its model. Your shopping list is sort of the same: your prediction of your future shopping that would be later met with the reality in the shop.
But how does it relate to the Bayesian logic? Its main logical proposition is that to build up a hypothesis one needs to have some priors. One needs to start somewhere to build a model being a brain as well. So the idea is that the brain has got wired in an explicit and pretty narrow set of assumptions about the reality.
So the brain is not only Bayesian; it is inherently biased.
Chivers expands his story into examples from popular culture such as seeing a different colours of a dress, visual illusions etc. He also goes as far as to repeat after Chris Frith calling the reality is "a controlled hallucination". I think it is a step too far in terms of definition of a word "hallucination" in this context. But it is not essential. Here is how he explains this idea:
He does it on the example of him having a cup of coffee that is unexpectedly got cold. He also goes on explaining how the brain corrects the mismatch between the expectation (or model; or hallucination depends what you prefer to use) and the sensory input. Though he somewhat loses an explanatory power in the process.
He also incorporates the conversation with Karl Firston and his daring that some scientists call "a unified brain" theory.
I find all of this is a very fascinating stuff. The book is a bit too wide-ranging and "popular-sciencey" but easy to read. There are not that many popular books on bayesian theory. So this one is a good starting point.
------
(1) the quotes are from a different book Ive read recently . The content of these two books overlaps ever so slightly but only in this particular idea of a brain as a generative model.
Recently with Covid we dealt with the another example of a bayesian thinking or the lack of it. If you have a covid test with 95% accuracy, and it came back positive. Does it mean the chance you have a Covid is 95%? The correct answer is "no". It is much lower as it also depends on the rate of prevalence in the population at the moment you've tested. There were many arguments at that time related to the incorrect interpretation of statistics. Some of them were pretty grim. For better examples and more explanation how this works I would recommend to read this book. Chivers explains it with the great clarity. I think he is a journalist rather than a scientist or mathematician. So the book is a little sketchy. It covers a lot of ground from the examples like that to the biography of Reverend Bayes. Also he interviews neuroscientists, psychiatrists and psychologists for this book.
The debate between the frequentists and the bayesians is not an empty one. It has a got a pretty fundamental applications for many serious things such as scientific method for example. The statistical experiment of testing hypotheses for the purpose of science is based on frequentist logic. The debate is raging for more than a century already. So far the frequentists prevail but they are losing ground, especially with emergence of an AI and so called replication crisis in science. Many of the hypotheses accepted are not confirmed when an experiment is replicated. The were a few scandals recently, most prominently in social psychology propagating different 'nudge' theories.
The chapter I was personally mostly fascinated with is about a hypothesis of Bayesian brain It is gaining ground between the neuroscientists as far as I understand but its root is more remote in the 19th century":
“In the nineteenth century, a German physicist and physician named Hermann von Helmholtz proposed a novel theory to explain the properties of perception. He suggested that a person doesn’t perceive what is experienced; instead, he or she perceives what the brain thinks is there—a process Helmholtz called inference. Put another way: you don’t perceive what you actually see, you perceive a simulated reality that you have inferred from what you see.� (1)
And nowadays some scientists think it is much broader than just perception. It is all cognition and emotions as well. Around 200 million years ago the mammals have evolved neocortex. This is where it properly starts. But because it is so complicated to summarise i would be really brief: the mammals’s brain produces a full 3d model of the reality. Based upon this model it can simulate different scenarios just in its head and predict future: both its own actions and the possible changes in the environment. Also it identifies the gaps between the model and the sensory input and try to minimise them either by adjusting the model or taking actions to adjust the environment closer to the model. Your imagination is also basically your brain playing its model. Your shopping list is sort of the same: your prediction of your future shopping that would be later met with the reality in the shop.
But how does it relate to the Bayesian logic? Its main logical proposition is that to build up a hypothesis one needs to have some priors. One needs to start somewhere to build a model being a brain as well. So the idea is that the brain has got wired in an explicit and pretty narrow set of assumptions about the reality.
"the neocortex may be prewired to assume that incoming sensor data, whether visual, auditory, or somatosensory, represent three-dimensional objects that exist separately from ourselves and can move on their own. Therefore, it does not have to learn about space, time, and the difference between the self and others. Instead, it tries to explain all incoming sensory information it receives by assuming it must have been derived from a 3D world that unfolds over time." (1)
So the brain is not only Bayesian; it is inherently biased.
Chivers expands his story into examples from popular culture such as seeing a different colours of a dress, visual illusions etc. He also goes as far as to repeat after Chris Frith calling the reality is "a controlled hallucination". I think it is a step too far in terms of definition of a word "hallucination" in this context. But it is not essential. Here is how he explains this idea:
"Instead of our image of the world coming in from our senses, our brains are making it up, constantly. We build a 3D model around ourselves. We’re predicting � hallucinating � the world. There’s not just a bottom-up stream of information � there is, vitally, a top-down one, as well. Higher-level processing in our brain sends a signal down, towards our nerve receptors, telling them what signals to expect."
He does it on the example of him having a cup of coffee that is unexpectedly got cold. He also goes on explaining how the brain corrects the mismatch between the expectation (or model; or hallucination depends what you prefer to use) and the sensory input. Though he somewhat loses an explanatory power in the process.
He also incorporates the conversation with Karl Firston and his daring that some scientists call "a unified brain" theory.
I find all of this is a very fascinating stuff. The book is a bit too wide-ranging and "popular-sciencey" but easy to read. There are not that many popular books on bayesian theory. So this one is a good starting point.
------
(1) the quotes are from a different book Ive read recently . The content of these two books overlaps ever so slightly but only in this particular idea of a brain as a generative model.
February 26, 2025
Thoroughly enjoyed the audiobook, very informative and fascinating without being dull or 'too much'. After having 'listened' to it, I catch myself explaining about certain things to the people in my life - with borrowed lines from the book (or at least the 'ideas'/Bayesian approach), so more than just 'entertaining', it's also sort of 'helpful'.
October 12, 2024
WOW, This was as pleasant as a blanket on a rainy evening.
For people trying to get Bayesian statistics better, or even learn what that is - the book is amazing, with great examples and perfect structure.
At the same time, it was not technical, and the audiobook version was like sitting next to a buddy telling you about his job, or research, that he is passionate about too.
For people trying to get Bayesian statistics better, or even learn what that is - the book is amazing, with great examples and perfect structure.
At the same time, it was not technical, and the audiobook version was like sitting next to a buddy telling you about his job, or research, that he is passionate about too.
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.
December 15, 2024
2.5 stars. If you've never read a book on Bayesian statistics, this book may be of interest to you -- but if you have (like me), you may find yourself bored to tears through science writer Tom Chivers' prolonged biography of Thomas Bayes and recapitulation of the theorem, extended philosophical musings, and various tangents on other topics like perception.
Further reading:
by Richard Harris (my absolute favorite book on this topic - see my review here
by Ben Goldacre
My statistics:
Book 306 for 2024
Book 1909 cumulatively
Further reading:
by Richard Harris (my absolute favorite book on this topic - see my review here
by Ben Goldacre
My statistics:
Book 306 for 2024
Book 1909 cumulatively
October 16, 2024
Excellent book! Highly recommend and I’m now a Bayesian! Only warning there is math and you will see every single thing in Bayesian terms not a bad thing at all
December 31, 2024
Really good use of examples to unpack Bayesian thinking in a way I'd not managed to grasp before.
The author claims that "once you understand Bayes, you start seeing it everywhere", and 2 days after completing the book I already had two light bulb moments.
First was that since moving in with my partner I'd got used to finding the odd clump of hair in the carpet - first time I saw one I jumped thinking it was a spider, but after a couple of months the sight became less alarming each encounter. Then yesterday I spotted one, calmly knelt down to pick it up, only for it to start scurrying towards me!
Second one is maybe a bit too determinisitic/not probabilistic enough to be Bayesian, but just noticed how much harder it was to increase the he average speed on my bike computer towards the end of the ride compared to at the start. The new data wouldn't move the needle as hard as I pushed!
The author claims that "once you understand Bayes, you start seeing it everywhere", and 2 days after completing the book I already had two light bulb moments.
First was that since moving in with my partner I'd got used to finding the odd clump of hair in the carpet - first time I saw one I jumped thinking it was a spider, but after a couple of months the sight became less alarming each encounter. Then yesterday I spotted one, calmly knelt down to pick it up, only for it to start scurrying towards me!
Second one is maybe a bit too determinisitic/not probabilistic enough to be Bayesian, but just noticed how much harder it was to increase the he average speed on my bike computer towards the end of the ride compared to at the start. The new data wouldn't move the needle as hard as I pushed!
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.
December 3, 2024
A fascinating explanation of Baye’s theorem and its potential explanatory power. The critique of frequentist statistics is compelling. And the extension of Bayesian thinking into AI, decision science, and consciousness is intriguing albeit not quite as persuasive. Perhaps because of my priors the author would argue.
October 23, 2024
Really nice easy to read introduction on Bayesian statistics.
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.
January 6, 2025
3.5, interesting but would have liked a more in depth review of bayesian applications. The second half of the book was very speculative and tried to persuade the reader how important bayesian statistics are. We got there by chapter 2 already!
November 6, 2024
Honestly more of a 2.5 star, barely eked out the 3 star rating. Very cool idea but he takes it too far. The brain and evolutions chapters seemed a bit too out there, personally. But the beginning is great, esp. when centered on science stats. I also really liked how he wove in a bit of history.
December 15, 2024
All hail Bayes.
February 3, 2025
Excellent history and explanatory text on Bayes; a way of thinking about probability with many helpful real world applications (including medicine!); update your priors! For more on the subject be sure to check out: and .
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 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.
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.
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 , rather than the complete worldview.
Claude's most fitting recommendation was , 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 : 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 : 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 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 :
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 , rather than the complete worldview.
Claude's most fitting recommendation was , 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 : 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 : 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 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 :
December 17, 2024
Two backpackers are lost. Wandering along a country lane, they meet a farmer idly leaning on a gate, chewing a grass stalk. 'Please Sir', asks one of the hapless pair, 'How do we get to Cromer?' 'Well', says the farmer, thoughtfully, 'I wouldn't start from here'. But I digress. Many years ago when the world was young I penned a polemic that attracted many brickbats. Among the many things that attracted the ire of the hip and fashionable was the assertion that, in science, no matter how many fancy schmancy statistics you use, you'll always end up with an estimate of probability that something or another is true, and after that you're on your own. I was accused of being something called a 'frequentist', and that was among the more polite epithets. I have since learned that there is a better way of doing statistics, and that relies on something called Bayes' Theorem, and the people who do statistics that way are called Bayesians. To this day I have never really understood Bayes' Theorem, and have, frankly, been deterred from learning by the fanatical adherence to their creed of its devotees (fanaticism of any kind being something of a turn-off). Imagine my delight when a good friend reviewed the book currently under discussion -- a guide to Bayes' theorem and an explanation of what the fuss was all about. Buoyed up by his stellar review I bought the book, imagining that the skies would clear, the scales would fall from my eyes, I would experience a Damascene Conversion, and then run naked through the streets of Cromer shouting 'Eureka'. (Nobody would mind. They are used to such things in Cromer). Well, it wasn't quite like that. I did learn a lot, but I am still rather confused. Perhaps I shouldn't have expected this to be a how-to book, with problems and worked examples (such books do exist). It's more of a history of a concept. However, as Chivers helpfully repeats throughout the book, frequentist statistics (I do hate these '-ists' and '-isms', I prefer to think of it as 'the statistics I was taught') says that you set up a hypothesis, gather some data, and ask 'how likely are we to see these data, given the hypothesis I've set up?' Bayesian statistics starts with the data, and ask which hypothesis it best supports. The crucial difference between the two is that Bayesian statistics starts with what's called a 'prior' -- that is, an idea based on what you already know, Ìýagainst which you test your data, and if the mismatch is unacceptably large, you add the new data into the pot and stir it round again, converging on a solution. If, for example, you are trying to work out the probability that a hypothesis might be true, there is no need to go in blindly. Instead, you can arm yourself with already established knowledge. So my hapless pair trying to get to Cromer mightn't have to ask the farmer at all -- if they have a map, a GPS, or have just seen a sign saying 'CROMER 2 MILES'. In a way, Bayesian statistics is the application of common sense. It is essential in things like drug trials, as Chivers explains. It has revolutionised work in evolutionary biology, my main concern in my day job (by day I'm with the Submerged Log Company), particularly the computation of evolutionary trees. Rather than put the genomes or observed traits of a whole load of fish and fowl into a computer and have to decide between the zillions of possible solutions that emerge, you can start by saying that you know from copious previous evidence that fish aren't fowl and whales are not insects that live on bananas, therefore discarding a lot of no-hoper solutions and can home in more quickly on the most plausible evolutionary tree. Chivers doesn't say anything about evolutionary trees, though he does discuss the history of Bayes and of statistics as a whole (very interesting) and bangs on at some length about how the brain is a Bayesian machine and that Bayes, like Love, is All Around (rather tedious). Although he discusses the enormous controversies that Bayesian statistics stokes, he doesn't really explain (to my satisfaction, but then I have a large posterior) why the fury is so, well, furious. So I am not sure I really learned a great deal more about Bayesian statistics than I knew before, and I certainly can't carry in my head (yet) a succinct explanation of why it's better than good old-fashioned statistics, for all that he repeats the mantra throughout. It's a diverting book, but perhaps I'll have to get one of those how-to guides with problems to work through and answers at the back of the book. This book is fun, for certain definitions of 'fun', but as the farmer said, I wouldn't start from here.
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April 12, 2025Book Review: Everything Is Predictable: How Bayesian Statistics Explain Our World by Tom Chivers
Introduction
In Everything Is Predictable: How Bayesian Statistics Explain Our World, Tom Chivers presents an engaging and accessible exploration of Bayesian statistics, elucidating its significance in interpreting the complexities of everyday life. Drawing on a wealth of examples from diverse fields, Chivers illustrates how this statistical framework enhances our understanding of uncertainty and decision-making processes. The book serves not only as an introduction to Bayesian methods but also as a compelling argument for their broader application in both science and everyday reasoning.
Content Overview
Chivers begins by contextualizing Bayesian statistics within the larger framework of statistical thought, contrasting it with the more conventional frequentist approach. He effectively breaks down the principles of Bayes� theorem, emphasizing the notion of updating beliefs based on new evidence. Through relatable anecdotes, Chivers demonstrates how Bayesian thinking permeates various aspects of life, from medical diagnoses to sports predictions and even personal relationships.
The narrative progresses by examining specific applications of Bayesian methods, highlighting their usefulness in fields such as epidemiology, economics, and artificial intelligence. Chivers adeptly discusses real-world case studies to showcase how Bayesian analysis can yield more nuanced insights compared to traditional statistical methods. He also reflects on the philosophical implications of Bayesian reasoning, questioning how our perceptions of knowledge and uncertainty shape our worldview.
Critical Analysis
One of the book’s most significant strengths is Chivers� ability to demystify complex concepts through clear explanations and engaging storytelling. His writing is approachable, making Bayesian statistics accessible to readers without a strong mathematical background. The use of real-world examples not only illustrates the practical applications of Bayesian methods but also captivates the reader’s interest.
Moreover, Chivers� enthusiasm for the subject matter is evident throughout the text, serving as a motivating factor for readers to appreciate the relevance of statistics in everyday decision-making. His thoughtful integration of personal anecdotes adds a relatable dimension to the book, allowing readers to connect with the material on a more emotional level.
However, some critics may argue that certain sections could benefit from a deeper exploration of the mathematical foundations underlying Bayesian statistics. While the book is primarily aimed at a general audience, including a more thorough examination of key equations or methodologies could add depth for readers interested in the technical details. Additionally, a more rigorous discussion of the limitations and potential pitfalls of Bayesian analysis would enrich the overall narrative.
Conclusion
Everything Is Predictable offers a refreshing perspective on the role of Bayesian statistics in understanding the world around us. Tom Chivers successfully blends engaging storytelling with insightful analysis, making a strong case for the importance of statistical reasoning in navigating uncertainty. The book encourages readers to rethink their approach to decision-making and highlights the power of Bayesian methods in various domains.
Recommendation
This book is highly recommended for academic libraries, statistics courses, and anyone interested in enhancing their understanding of data analysis. Its interdisciplinary approach makes it suitable for a wide audience, including students, professionals, and general readers who seek to grasp the relevance of statistics in everyday life. Chivers� ability to render complex ideas into accessible narratives ensures that Everything Is Predictable will resonate with readers and inspire further exploration of Bayesian statistics.
Introduction
In Everything Is Predictable: How Bayesian Statistics Explain Our World, Tom Chivers presents an engaging and accessible exploration of Bayesian statistics, elucidating its significance in interpreting the complexities of everyday life. Drawing on a wealth of examples from diverse fields, Chivers illustrates how this statistical framework enhances our understanding of uncertainty and decision-making processes. The book serves not only as an introduction to Bayesian methods but also as a compelling argument for their broader application in both science and everyday reasoning.
Content Overview
Chivers begins by contextualizing Bayesian statistics within the larger framework of statistical thought, contrasting it with the more conventional frequentist approach. He effectively breaks down the principles of Bayes� theorem, emphasizing the notion of updating beliefs based on new evidence. Through relatable anecdotes, Chivers demonstrates how Bayesian thinking permeates various aspects of life, from medical diagnoses to sports predictions and even personal relationships.
The narrative progresses by examining specific applications of Bayesian methods, highlighting their usefulness in fields such as epidemiology, economics, and artificial intelligence. Chivers adeptly discusses real-world case studies to showcase how Bayesian analysis can yield more nuanced insights compared to traditional statistical methods. He also reflects on the philosophical implications of Bayesian reasoning, questioning how our perceptions of knowledge and uncertainty shape our worldview.
Critical Analysis
One of the book’s most significant strengths is Chivers� ability to demystify complex concepts through clear explanations and engaging storytelling. His writing is approachable, making Bayesian statistics accessible to readers without a strong mathematical background. The use of real-world examples not only illustrates the practical applications of Bayesian methods but also captivates the reader’s interest.
Moreover, Chivers� enthusiasm for the subject matter is evident throughout the text, serving as a motivating factor for readers to appreciate the relevance of statistics in everyday decision-making. His thoughtful integration of personal anecdotes adds a relatable dimension to the book, allowing readers to connect with the material on a more emotional level.
However, some critics may argue that certain sections could benefit from a deeper exploration of the mathematical foundations underlying Bayesian statistics. While the book is primarily aimed at a general audience, including a more thorough examination of key equations or methodologies could add depth for readers interested in the technical details. Additionally, a more rigorous discussion of the limitations and potential pitfalls of Bayesian analysis would enrich the overall narrative.
Conclusion
Everything Is Predictable offers a refreshing perspective on the role of Bayesian statistics in understanding the world around us. Tom Chivers successfully blends engaging storytelling with insightful analysis, making a strong case for the importance of statistical reasoning in navigating uncertainty. The book encourages readers to rethink their approach to decision-making and highlights the power of Bayesian methods in various domains.
Recommendation
This book is highly recommended for academic libraries, statistics courses, and anyone interested in enhancing their understanding of data analysis. Its interdisciplinary approach makes it suitable for a wide audience, including students, professionals, and general readers who seek to grasp the relevance of statistics in everyday life. Chivers� ability to render complex ideas into accessible narratives ensures that Everything Is Predictable will resonate with readers and inspire further exploration of Bayesian statistics.
February 1, 2025
The book is a description of Bayesian statistics, mostly as a contrast to more common "frequentist" models. The book is NOT heavy on math, but is more interested in the general implications of Bayesian statistics as well as the fundamental concepts.
Without going too deep into it, the first sections really describe the history of Bayesian theory and generally what it is. The short version is that Bayesian statistics differs from what most of us are familiar with in that you start off with some base assumptions and use data to adjust your prior assumptions as it comes in. So, for example, if I think it will take me 15 minutes to get to the grocery store and the first time I go it takes me 25, standard statistical models would say that I have to assume it is 25 minutes for future estimates (with really wide error bars). Bayesian methods would just shift the probability to something slightly higher than 15 minutes but not go the full way to 25, depending on how strong my assessment of my initial assumptions is. As time goes on, I may see that the 25 minutes was a fluke, or I may see that my initial assumptions were invalid, but either way as we continue to collect data eventually the two methods will merge.
I first learned about Bayesian models in college, and while we didn't use it a lot it does make some sense for things like engineering where you aren't really starting an experiment with a blank slate. Standard frequentist proponents generally don't like Bayesian methods because there is a lot of leeway on selecting priors, which can change your answer. The Bayesian response is that the frequentists are doing the same thing by assuming a "flat" prior, just not explicitly, and in many cases that interpretation makes less sense.
Chivers goes on to discuss some different aspects of the theory and how it can help with the p-hacking and other concerns that have been raised about scientific research in the past couple of years. I think he does a good job of showing that using a more Bayesian approach would help with some aspects of the problem, but there are some (like outright fraud) that would need to be addressed through other methods.
I thought the weakest part of the book was in the last 1-2 chapters where Chivers starts applying Bayes' theorem in lots of places outside of traditional statistics, including overall brain function. While I'm sure there may be some truth to what he states, a lot of it seems like trying to fit everything into a Bayesian construct where there is very little support. Honestly, if you skip the last chapter I don't think you are missing much.
As far as the writing overall, Chivers is very readable. He doesn't get a lot into the math of things, which I personally would have liked but I understand puts a lot of folks off. The book flows well and he gives great examples in a very conversational style.
I liked the book, thought it was a fun, relatively fast read, and would recommend it to anyone interested in statistics through a very non-math-heavy lens.
Without going too deep into it, the first sections really describe the history of Bayesian theory and generally what it is. The short version is that Bayesian statistics differs from what most of us are familiar with in that you start off with some base assumptions and use data to adjust your prior assumptions as it comes in. So, for example, if I think it will take me 15 minutes to get to the grocery store and the first time I go it takes me 25, standard statistical models would say that I have to assume it is 25 minutes for future estimates (with really wide error bars). Bayesian methods would just shift the probability to something slightly higher than 15 minutes but not go the full way to 25, depending on how strong my assessment of my initial assumptions is. As time goes on, I may see that the 25 minutes was a fluke, or I may see that my initial assumptions were invalid, but either way as we continue to collect data eventually the two methods will merge.
I first learned about Bayesian models in college, and while we didn't use it a lot it does make some sense for things like engineering where you aren't really starting an experiment with a blank slate. Standard frequentist proponents generally don't like Bayesian methods because there is a lot of leeway on selecting priors, which can change your answer. The Bayesian response is that the frequentists are doing the same thing by assuming a "flat" prior, just not explicitly, and in many cases that interpretation makes less sense.
Chivers goes on to discuss some different aspects of the theory and how it can help with the p-hacking and other concerns that have been raised about scientific research in the past couple of years. I think he does a good job of showing that using a more Bayesian approach would help with some aspects of the problem, but there are some (like outright fraud) that would need to be addressed through other methods.
I thought the weakest part of the book was in the last 1-2 chapters where Chivers starts applying Bayes' theorem in lots of places outside of traditional statistics, including overall brain function. While I'm sure there may be some truth to what he states, a lot of it seems like trying to fit everything into a Bayesian construct where there is very little support. Honestly, if you skip the last chapter I don't think you are missing much.
As far as the writing overall, Chivers is very readable. He doesn't get a lot into the math of things, which I personally would have liked but I understand puts a lot of folks off. The book flows well and he gives great examples in a very conversational style.
I liked the book, thought it was a fun, relatively fast read, and would recommend it to anyone interested in statistics through a very non-math-heavy lens.
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.
January 4, 2025
I picked this one after hearing about it on a Financial Times podcast. Being a data science professional, it piqued my interest and I wanted to read it.
It's a very interesting book about the impact of Bayes theorem in our lives and its presence in our world. Through this book, Chivers has tried to shed light on its omnipresence in our day to day lives and how we are unintentionally acting as a Bayesian system when making decisions in our lives. Right from the smallest of small decisions to big life decisions.
It's very informative and for someone who's never heard of Bayes or probabilities and their role in our life, this book is a go-to book that I'd recommend. Some of the terminology would be a bit difficult to grasp for people who're unfamiliar with statistical terms like precision, specificity etc. But overall, the writer has done a good job at explaining every concept or idea in a simple and straightforward manner.
Personally, I loved the chapters titled Bayesian Science and The Bayesian Brain. Some very fascinating ideas were discussed in those chapters about how our prior beliefs shape how we view the world and our actions and decisions. And how Bayes theorem is at the heart of these decisions that we make. What the book did for me was make me further curious about reasoning and consciousness and the science of rational thinking. I have added a couple of books and authors who I'd like to read up on.
The only thing that I didn't like about this book was that I felt it was repetitive and trying to show how Bayes theorem is playing a significant role in almost every chapter. But I guess that was the whole point of this book. Additionally, I feel the chapter dedicated to the war between frequentists and bayesians could have been kept short.
I'd surely recommend this to every data professional as well as anyone who wants to understand how probabilities play a vital role in shaping our world and our understanding of it.
It's a very interesting book about the impact of Bayes theorem in our lives and its presence in our world. Through this book, Chivers has tried to shed light on its omnipresence in our day to day lives and how we are unintentionally acting as a Bayesian system when making decisions in our lives. Right from the smallest of small decisions to big life decisions.
It's very informative and for someone who's never heard of Bayes or probabilities and their role in our life, this book is a go-to book that I'd recommend. Some of the terminology would be a bit difficult to grasp for people who're unfamiliar with statistical terms like precision, specificity etc. But overall, the writer has done a good job at explaining every concept or idea in a simple and straightforward manner.
Personally, I loved the chapters titled Bayesian Science and The Bayesian Brain. Some very fascinating ideas were discussed in those chapters about how our prior beliefs shape how we view the world and our actions and decisions. And how Bayes theorem is at the heart of these decisions that we make. What the book did for me was make me further curious about reasoning and consciousness and the science of rational thinking. I have added a couple of books and authors who I'd like to read up on.
The only thing that I didn't like about this book was that I felt it was repetitive and trying to show how Bayes theorem is playing a significant role in almost every chapter. But I guess that was the whole point of this book. Additionally, I feel the chapter dedicated to the war between frequentists and bayesians could have been kept short.
I'd surely recommend this to every data professional as well as anyone who wants to understand how probabilities play a vital role in shaping our world and our understanding of it.
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