The Art of Uncertainty: How to Navigate Chance, Ignorance, Risk and Luck

by David Spiegelhalter

From the UK’s ‘statistical national treasure’, a clever and data-driven guide to how we can live with risk and uncertainty

Life is uncertain. We are all the result of an unforeseen and unforeseeable sequence of small occurrences. But what underlies this fragile chain of events? Is it random or just complex? And what role does luck play in our lives?

David Spiegelhalter has spent his career crunching data in order to help understand uncertainty and assess the chances of what might happen. In The Art of Uncertainty, he gives readers a window onto how we can all do this better.

Uncertainty, he argues, is a relationship between the observer and an object in the outside world. He shows us how we can express it numerically, and then update our beliefs about the future in the face of constantly changing experience. In crystal-clear prose, he takes us through the principles of probability, a field that informs everything from annuities to pandemics and climate change, while also examining the limitations of statistical modelling and arguing we need to have the humility to admit our ignorance.

Drawing on a wide range of real-world examples, this is an essential guide to navigating uncertainty in a world that makes it inevitable.

Genres: Nonfiction, Science, Mathematics, Psychology, Economics, Business, Finance

336 pages, Hardcover

First published September 19, 2024

About the author

Sir David Spiegelhalter has been Winton Professor of the Public Understanding of Risk at the University of Cambridge since October 2007. His background is in medical statistics, with an emphasis on Bayesian methods: his MRC team developed the BUGS software which has become the primary platform for applying modern Bayesian analysis using simulation technology. He has worked on clinical trials and drug safety and consulted and taught in a number of pharmaceutical companies, and also collaborates on developing methods for health technology assessment applicable to organisations such as NICE. His interest in performance monitoring led to his being asked to lead the statistical team in the Bristol Royal Infirmary Inquiry, and he also gave evidence to the Shipman Inquiry.

Reviews

[Richard Marney · Rating 5 out of 5]

I read this book through twice. The first at a quick coffee shop pace and the second delving more deeply into the subject matter.

Much of the material has been covered elsewhere in the vast literature on the general topic area, but the author distinguishes himself in the quality of the organization and writing. The book makes it to the reference library!!!

[kxtera meddins (maresh) · Rating 4 out of 5]

4.5
should be essential reading

[Rory · Rating 3 out of 5]

I am very interested in the topic, but I like clarity of communication: the author leans towards words that are not in common usage, and that somewhat foggy style of communication takes away from the accessibility of the text.

The chapters dealing with uncertainty, and with guidance for the communication of uncertainty, were the most impactful; there were some excellent takeaways that straddled a line between statistical analysis and crisis management, and the writing style was far less dense than in the preceding chapters. This aspect of the book was more resonant than the sections that came before, which were more mathematically oriented, and not very well presented.

[Kate · Rating 4 out of 5]

I’ve always hated statistics, especially at uni, but I love this author so I struggled through just for him

[Ali · Rating 4 out of 5]

I like evidence, and I enjoy learning, and as such, I like turning uncertainty into certainty - or at least working out how to understand - so this book was a real joy for me. Spiegelhalter starts with a basic understanding of probability, and moves on to look at various practical applications from seeking to understand what is unknown, through to prediction of events small and not so small. The book refers at times to some of the most pressing issues around prediction, from climate change to probable future pandemics, but the star here is the process of understanding and making this chaotic world just a tiny bit more predictable. There is some mathmatical concepts, but it is formula-lite if not formula-free.

[Nacho · Rating 3 out of 5]

Solid read , a great deep dive into uncertainty in a digestible way. IMO the author was aiming to structure his chapters like a Malcom gladwell book and I would say he got 65% of the way there . The examples used to build up concepts and unpack probabilities/uncertainty were good but I felt they never expanded enough . The author engaged with the example enough to intrigue but never enough to satisfy . However there are fantastic chapters that I would pluck out

[Marie Clarke · Rating 4 out of 5]

I think this would be better read rather than listened to. Some fabulous facts and interesting stand points. Heavy on the statistics as should be expected, all very well explained but will need another listen.

[Chad Manske · Rating 4 out of 5]

David Spiegelhalter’s “The Art of Uncertainty: How to Navigate Chance, Ignorance, Risk and Luck” offers a masterclass in understanding and embracing the unpredictable nature of our world. Spiegelhalter, a renowned statistician, doesn’t simply teach probability—he reframes uncertainty as a deeply personal relationship between ourselves and the unknown, challenging the reader to see uncertainty not as a flaw in our knowledge, but as an inevitable feature of existence.
**Uncertainty as Personal**
Spiegelhalter argues that uncertainty isn’t an objective property of the world, but a reflection of our own knowledge and perspective. What’s uncertain to one person may be obvious to another, depending on their background and information.
**Quantifying the Unknown**
The book urges readers to move beyond vague terms like “likely” or “possible.” Spiegelhalter demonstrates how expressing uncertainty numerically—using probabilities—can clarify thinking and communication, especially in fields like medicine, climate science, and public policy.
**Probability, Risk, and Luck**
Through lively prose and real-world examples, Spiegelhalter explores the principles of probability, the difference between hazard and risk, and the role of luck in shaping outcomes. He illustrates how misinterpretations of probability have led to historical blunders, from the Bay of Pigs to maritime disasters.
**Decision-Making and Emotional Responses**
The book delves into the psychological side of uncertainty, showing how our emotions and biases shape decisions. Spiegelhalter offers strategies for making better choices under uncertainty, including updating beliefs as new evidence emerges—a nod to Bayesian reasoning.
**Communicating Uncertainty**
Spiegelhalter emphasizes transparency and honesty, advocating for clear language and visual aids to help others grasp complex risks and probabilities.
This isn’t a breezy self-help manual—it’s a rigorous, yet accessible, exploration for anyone interested in statistics, science, or simply making smarter decisions in a complex world. Teachers, business leaders, and curious readers alike will find Spiegelhalter’s wealth of relatable examples and practical wisdom invaluable. “The Art of Uncertainty” ultimately teaches us to be humble in the face of the unknown—and to find empowerment, not fear, in life’s unpredictability.

[Marie Edlund · Rating 4 out of 5]

Detta är en bok som tar ett större grepp om statistik än bara beräknings teknik. Spännande och viktiga tankar att ta med sig.

[Marnix Verplancke · Rating 4 out of 5]

Wij mensen zijn de speelbal van het toeval en de onzekerheid. Als je moeder en je vader elkaar niet hadden ontmoet, was je er nooit geweest. En dat je hier bent geboren en niet in Gaza heb je ook niet zelf gekozen, net zomin als je genetische aanleg voor een of andere kwaal. En dat is nog maar het begin, want een mensenleven bestaat voor een groot deel uit keuzes maken. Wat je gaat studeren, welke job je aanvaardt en of je nu wel of niet in zee wil met die man of vrouw waar het mee klikt, waarna er misschien kinderen komen en alles van voor af aan herbegint. Hoe gaan we om met die onzekerheid en op welke basis maken we de beste keuzes? Statisticus David Spiegelhalter schreef er een verhelderend boek over, The Art of Uncertainty, How to Navigate Chance, Ignorance, Risk and Luck.

[Karlis Skulte · Rating 3 out of 5]

There were a few interesting topics and discussions such as reframing how general descriptions of likelihood vs probability can be easily misunderstood without supporting data and how confidence weighted decision making can shine a light on degree of certainty. However, fairly long sections of the book read as a textbook with detailed explanations of statistics and probably methodology and calculations and were a bit of a bear to push through. There are warnings about this in the beginning of the book, so it shouldn’t come as a surprise.

[Alok Bharadwaj · Rating 5 out of 5]

Uncertainty has certainly marked the first half of 2020's. Starting with the Pandemic, wars, and the changing technological landscape - this decade has made sure that humans have to live through some of the most uncertain years of their lives. Against this backdrop, a renowned statistician comes with a timely book teaching us how to "think" about uncertainty.

David Spiegelhalter makes a convincing case that uncertainty is a "relationship", and not an objective feature of the world. This requires some thinking through. What exactly does it mean? It means, for one, every one of us could have different degrees of uncertainty regarding the same set of data. Why? Because we all live through different lives, and have consequently developed different "inner models" of how the world works. We literally see the world differently.

The fact that everyone of us have different biases, and perspectives need not alarm us. In fact, it might very well be humanities greatest strength. As David explains, the best decisions are made when we combine predictions from different independent models. In that spirit, we should all welcome uncertainties and not try to hide it. We should make space for people to voice out differences in opinion, so that we atleast understand what the range of plausible models are out there.

The book does not aim to be a self-help book. However, given the nature of the topic, it cannot help but delve into some personal advice. Given that the world we live in is increasingly complex, it is almost guaranteed that we have to confront what David calls "Deep Uncertainties". These are the class of uncertainties for which, it's not just a matter of not having empirical data but rather we don't even have a proper model to establish some baseline priors. In various other works they are called "Black Swan" events, those which are far outside the norm.

The personal narrative that we tell ourselves provides us with the direction with which we need to act in such circumstances. When numbers fail us, stories show the light. It is therefore all the more important that we are able to reflect on what kind of stories we tell ourselves, since that defines how we act in the face of deep uncertainty.

[fish_fin · Rating 5 out of 5]

A fun read, lots of interesting anecdotes on how statistics is used and how it should be used.

[Gijs Limonard · Rating 3 out of 5]

There is absolutely nothing wrong with this work on probability, only that it is pretty generic and boring. For the interested reader for the first time dipping his/her toe into the literature on probability theory this suffices as a decent primer; for all others please refer to these excellent works: all the books by Taleb Nassim Nicholas and Bernoulli's Fallacy: Statistical Illogic and the Crisis of Modern Science.

[Robin Perkins · Rating 3 out of 5]

I received this book as part of a Goodreads giveaway.


This is a text full of information. However, it can be a difficult read as it is presented very straightforward and mechanical. The examples are solid, but are presented mechanically. It makes the book very dry to read and can get long-winded at times. When picking this text up know it reads more like a textbook than a casual read book.

[Brian Clegg · Rating 5 out of 5]

There's something odd about this chunky book on probability - the title doesn't mention the P word at all. This is because David Spiegelhalter (Professor Sir David to give him his full title) has what some mathematicians would consider a controversial viewpoint. As he puts it 'all probabilities are judgements expressing personal uncertainty.' He strongly (and convincingly) argues that while the mathematical approach to probability is about concrete, factual values, outside of the 'natural' probabilities behind quantum effects, almost all real world probability is a subjective experience, better described by more subjective terms like uncertainty, chance and luck.

A classic way to distinguish between those taking the frequentist approach to probability and the Bayesian approach is their attitude to what the probability is of a fair coin coming up heads or tails after the coin has been tossed but before we have looked at it. The frequentist would say it's definitely heads or tails, but we can't say which. The Bayesian would say it's still 50:50 because we don't have any information yet. Spiegelhalter puts himself firmly into the Bayesian camp. However, even the most rabid frequentist could not find issue with Spiegelhalter's careful and detailed introduction to the nature of probability and how we use it.

There are plenty of real world examples here, from Covid-19 risks to picking socks at random from a drawer. Spiegelhalter provides us with a range of stories to back these examples up, making large parts of the content highly readable. If I have a criticism, I think the book is too long and could have had a tighter structure. I felt myself drifting away from interest and skipping through a few pages (it is over 400 pages long) occasionally - but always came back into focus as a new topic was covered.

As was the case with its earlier companion, The Art of Statistics, this is not going to turn you into an expert. Although there is some gentle mathematics, there is nothing more complicated than getting your head around conditional probability representations - but there is no doubt that reading the book will give you a better idea of what probability is, how it's used and abused, and why we can be more precise about some predictions than others. You will have to work a little to absorb what's in here - but it's worth the effort.

I think this pair of books should become classics, very much in the tradition of the Pelican imprint, which always been intended to inform non-experts without patronising. If you've ever heard Spiegelhalter speak, everything is put across in a warm, favourite uncle fashion - this is the case with the best parts of his writing too. It's a voice of reason in an area that can sometimes seem counter-intuitive, and it is very welcome.

[Ben]

My Dad got me this book after I got a job as an actuary and I worried that it would contain no information whatsoever that I didn't already know. However I ended up actually learning some things, which is a relief. Mostly soft things, like the fact that all probability is an expression of a relationship between an observer and the world, an expression of uncertainty given your information, rather than anything real in the world, or the fact that when a statistician gives a p-value to an observation, that value assumes the correctness of the model, which is itself uncertain, and this can be hard to account for. It's not that I didn't think these things before, but it's nice to have insights like these stated precisely and then elaborated on by a person with a lifetime's expertise in the subject. I also gained some harrowing examples to support my existing opinions on how poor an average (or even a supposedly smart) person's understanding of maths often is. E.g. a supposed "expert" arguing in court that, because the probability of a given baby dying of sudden infant death syndrome (SIDS) was 1/8543, the probability of it happening twice in one family with two children is (1/8543)^2, which is roughly 1 in 73 million, and therefore this is the probability that a mother both of whose children supposedly died of SIDS didn't instead murder her children. This not only assumes that the events are independent, which they obviously wouldn't be, but more importantly it ignores how unlikely a given mother is to murder her children and ignores any other possible causes of the deaths. It literally assumes that, given all families with two children, both of whom die in infancy with no apparent cause, 1 in 73 million have both children dying of SIDS, and all the rest have both children murdered by their mother. Obviously ridiculous, but this particular mother (Sally Clark) was actually sentenced and served more than three years in prison. Upon being released she drank herself to death, as I'm sure I would have. Meanwhile the idiot who supplied this argument in court is still alive and has been knighted!

In the last 3 non-fiction books I've read I've noticed typos, which makes me want to start keeping track. I found 4 typos in this book. On page 145 the "teams" in "those teams at the top of the table" should instead be "leagues". On page 273 the expression (RR-1)/R should instead be (RR-1)/RR. On page 322 there is a table with one entry being "Makes born in 2045" which should be "Males born in 2045". On page 338 there is a graph where the x axis goes 0, 5, 10, 15, 20, 20 which should instead be 0, 5, 10, 15, 20, 25.

[Mikala · Rating 3 out of 5]

I switched my major in college from biology to chemistry specifically to avoid taking additional statistics courses. I excelled in all upper division math classes, but statistics was too boring to survive. Of all the college courses, it is the most applicable to life. Like learning to balance a budget or get signatures from 6 professors when 4 of them are on sabbatical so you can graduate on time, having an innate grasp on statistics would set you on a path of a lifetime of success - if somewhat boring success.
All this is to say, I found this book the same as those college courses. Tedious to the point of absurdity. Yes, it's true I don't understand statistic. Yes, you can say 1 out of 10 or 10% and my brain knows it's the same thing but the emotions are different if we're talking about the lottery odds or cancer risks. The book tries hard to make you understand that these are the same stats with repetitive and occasional dull stories about taxes. Imagine behavioral economics before the "behavioral" part - before Freakonomics. It's just a lot of statistical analysis geeks hanging around in a convention hall talking spreadsheets and error bars.
This is a good book for someone that already is into statistics or someone who might want a career in actuarial sciences. For the "rest of us," I'll wait for a decent podcast about it and keep messing up statistics every time I hear the news.

[Andy · Rating 3 out of 5]

Overall the author does a superior job of explaining some complex topics, but it's not clear to me what the audience is. For scientists, much of this might be tedious. On the other hand, for non-scientists it might be too technical.
I thought his examples were odd. For example, with COVID medications, he got into the weeds on one study of steroids to explain how we know that they worked. This is not super-exciting cutting edge stuff, since an old rule of thumb in medicine is that "No patient should die without the benefit of steroids." (There is a variation on this in The House of God.) But okay, it's making an important point: here's how we generate hard evidence for how to help people, even in the middle of a crisis. What's missing though, is the other side of the coin: how do we know, for instance, that Ivermectin didn't work? This kind of contrast is where one can get into the critical thinking needed to navigate interpretation of evidence.

[Wing · Rating 5 out of 5]

With the exception of quantum phenomena, probability does not exist independently of our perception and cognition. Our approach to it should always be Bayesian. It will, therefore, always require modelling. And insofar as modelling is ontologically distinct from reality, all models are, in a sense, wrong, and uncertainty will always be intrinsic and not eradicable. Taking all of these factors into account will provide us with a sound way to deal with forecasts and risks. The book is well-written and comprehensive. The mathematics in the early chapters are clear and easy to follow. However, later chapters cover deeper topics, and the mathematics are not really explained in detail, but I sense that this is a conscious decision made by the author. His frequent wry humours make the already superb book even more delightful. It is as good as the other Pelican books written by the same author. Five stars.

[Alberto Meucci · Rating 4 out of 5]

This was the first book I read by Spiegelhalter, and I found his work to be highly insightful, with a sharp and critical perspective.

The book offers a thoughtful exploration of life's randomness, illustrating how events we consider rare are often not as uncommon as they seem, and how luck is simply a matter of numbers.

At its core, the author presents the idea that uncertainty is subjective—a refreshing perspective that has greatly enhanced my understanding of probability and uncertainty, particularly in my professional work.

Overall, I highly recommend this book to anyone interested in delving deeper into how probability—an abstract concept existing only in our minds—can profoundly influence our beliefs and decisions in life.

[Davidg · Rating 4 out of 5]

This slightly falls between two stools: becoming too technical for the ordinary reader but not detailed enough for the mathematician/statistician. As it is 47 years ago that I was taught statistics by Spiegelhalter’s supervisor, I am more than a little rusty on the equations etc that I once used to know. Therefore, some of the technical details were beyond me now.

However, the more philosophical arguments (eg, probability doesn’t exist) and the many examples he gives are excellent. Both personal choices and national and international decision making process is examined and the statistical processes that can be used to help.

Enjoyable and thought provoking.

[Nicola Waters · Rating 2 out of 5]

I did a maths degree, and stats and probability were always one of my favourite parts. But professionally I’ve mostly had no cause to study further because maths is tangential to my job at best. You’d think therefore I might be the ideal reader for such a book- and at first seemed very promising, nice refresher on the stuff I always liked around calculating probability. But I couldn’t finish it- more and more detail that felt like it belonged more in a textbook. Might be a failing on my part, but my suspicion is, if a maths grad who always enjoyed this subject are struggled with it, then a complete layman would be lost.

[Stuart Trow · Rating 5 out of 5]

There have been a number of books shedding light on the use and abuse of statistics and misunderstandings related to probability and human biases. This is one of the best and could easily (and usefully) be read alongside “May Contain Lies” by Alex Edmans. There is nothing earth-shattering about the material, it is just presented as accessibly as possible given the concepts involved. The narrative and relatable examples help to make those concepts easier to absorb than they might have been in a drier book.

[Henrik · Rating 3 out of 5]

Spiegelhalter is undoubtedly a formidable statistician and the book richly illustrates his craft with many real life examples. It is quite technical in parts (even for me with a MSc Econometrics degree). I think the book however fails to make use of these technical passages and they could to some extent have been left out. To me the book falls in between the cracks of being neither a research/learning book (not rigorous enough) nor a practitioner guide (with more applications of theory to a broader range of real world topics).

[Shen Xu · Rating 3 out of 5]

An informative book on hazard, risks, probabilistic forecasting, how to communicate all of these, and more.
The examples and questions are interesting, though there were a lot of references to COVID-19, which is unavoidable considering the relevancy of the topic. There are summaries at the end of each chapters to capture the main points (useful of skimmers).
It also touched upon AI and its uncertainty and the author confirmed that he also used LLM to support his writing of this book, an honest and welcoming point.

[Manish · Rating 3 out of 5]

“The oldest and strongest emotion of mankind is fear, and the oldest and strongest kind of fear is the fear of the unknown” - HP Lovecraft
People who are good at predicting (per Brier’s rating - meaning if wrong, the -ve score is much higher):
Aggregation: use multiple sources of information
Meta-cognition: they have insight into their own thinking and therefore are aware of their biases
Humility: willingness to acknowledge uncertainty
Did not finish - too dry, too much math

[Writemoves · Rating 2 out of 5]

I am sure that this is an excellent book for many people. However, my lack of understanding and knowledge of statistics made my likelihood of enjoying this book "improbable." There were small bits of information and observation that I was able to glean – –for example, I found his analysis on Covid, statistics enlightning. But frankly, I struggled through all the numbers and calculations. I took a chance, but was not able to navigate through the book.

[E · Rating 2 out of 5]

The book starts out well with discussions of probability and chance, moving on to Bayes' Theorem and other elements of statistics. But then the author suddenly becomes much more vague and provides rather anodyne anecdotes about risk assessment.

Maybe a shorter and thus more focused volume would have been more helpful. Spiegelhalter seems like a stellar mathematician and probably a worthwhile consultant. But this book could have been better.

[Keith Gardiner · Rating 4 out of 5]

We are presented with recommendations and judgments based on probabilities every day but until reading this book I didn’t have much of a framework for considering these claims and how reliable they are. I feel like I have learned from this book and for that I am grateful. I read it in hardcover but an e-book would have made it easier to look up the words I didn’t know…