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The Art of Uncertainty - David Spiegelhalter *****

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.

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