Skip to main content

Bayes' Rule - James V. Stone ***

Of all the areas of mathematics, probability is arguably the most intriguing to the non-mathematician, and this is particularly the case with Bayesian analysis, which can be delightfully counter-intuitive. However, the more complex aspects can be tricky to get your head around, so I was delighted to have the chance to read this book, subtitled 'a tutorial introduction to Bayesian analysis.'

 I need to say straight away that this isn't really a popular science title, and the author is very clear about this - it's a kind of textbook lite - but if you have found out a bit about Bayes this book is an opportunity to dive into it a little deeper without taking on the full rigour of a textbook approach. Why should you care? Bayes gives us a mechanism that enables us to do things like go from a known piece of information like 'what's the probability of a symptom given a disease' to estimate a much more interesting unknown like 'what's the probability of the disease given a symptom' - an extremely powerful mechanism.

 James Stone does his best to accommodate us ordinary folk. The book opens well, apart from a bizarrely heavy smattering of references on page 1, with a gentle introduction, and keeps the mood light after the classic disease application by looking for a mechanism of determining whether some said 'four candles' or 'fork handles' in the Two Ronnies style. If you are prepared to make an effort, for most of us probably a considerable effort, you will go on to pick up a lot more about using Bayes than you already knew (if you aren't a mathematician).

 It is rather unfortunate for the general reader, though, that the book obeys the rules of the textbook rather than a popular science exposition. This comes across in unnecessary use of terminology - defining things that, frankly we don't need to know - and in rapidly moving to using symbols in equations, where they are rarely necessary at this level and all they do is put readers off. I suspect the moment that Stone introduced the Greek letter theta (θ) he made things ten times harder - unless you do this kind of thing every day, suddenly the text gets far less readable - the eyes bounce off it.

 Even though I enjoyed the fork handles, I also thought the choice of examples could have been better. It was okay to use disease and symptom once, as it's an important application, but most of us rarely have to deal with this kind of situation and it would have been better to use more personally relevant applications. It was also unfortunate that when explaining random variables Stone chose a coin which is 90% likely to be heads and 10% likely to be tails - there is too much baggage attached to coins being 50:50. It would have been less confusing to have something that we might encounter (a scratch card, say) that is likely to be one value 90% of the time and the other 10%.

 If you make it to the final chapter you are rewarded with a very readable, if too brief, introduction to the distinction between Bayesian and frequentist approaches, and just a touch of the mind bending capabilities of Bayesian thinking. With a bit more of this contextual material throughout the experience would have been gentler and more enjoyable - but even as a closer to the book it provides interesting material.

 Don't expect, then that this book will make fun, popular science bedtime reading. It's not that kind of exercise. However, if you are prepared to overcome the onslaught of thetas and don't mind reading some statements several times to get what's being said, it is an excellent way to expand a vague understanding into a more sound knowledge of the basic mechanics of Bayesian analysis.
Paperback:  
Using these links earns us commission at no cost to you

Buy direct from the author: Click here
See one of the mind-bending implications of Bayes' rule in our feature.
Review by Brian Clegg
Labels:

Comments

Post a Comment

Popular posts from this blog

Beyond Belief - Helen Pearson *****

Apparently it comes as a surprise to many that medicine was not particularly scientific until the end of the twentieth century (to be honest, it's no surprise to me - we had a GP who used homeopathy in the 90s). Instead it was based on anecdotal guidance - the kind of thing that appeared to work. Evidence-based medicine has since improved the field, trying where possible to base decisions on evidence, ideally based on randomised controlled trials. The first part of Helen Pearson's book covers this well - though I think it's by far the least interesting part of what we discover. Instead what's truly fascinating is the rest of it, looking at a wide range of other fields where evidence was rarely properly used and that are only now starting to dip a toe in the water. These include social policy, policing, conservation, business and education. The main part of the book gives us examples of how bad these areas have been in terms of basing decisions on what's always been ...
Post a Comment
Read more

The Infinite Book – John D. Barrow ****

Authors are often asked to review books on a topic they’ve written on themselves. The reasoning is sensible – they ought to know something about the subject – but there’s always that uneasy suspicion that there’s going to be a bit of bias creeping in. So I think it’s only fair to admit up front that I have written a book on infinity (of which more later). Infinity is a wonderful subject, because it’s intimately mind-bending (if the combination sounds paradoxical, that’s what infinity is all about) and gives you the chance to pull in all sorts of different concepts and assocations along the way, something Barrow does with great gusto. There’s a surprisingly large amount of coverage here for God, and for the universe, and the book jumps around from Aristotle to Hilbert’s Infinite Hotel (explained at great length), from the paradoxes of infinite sets to the paradoxes of time travel. Overall it’s an enjoyable journey that gives plenty of opportunity to be amazed and surprised. The...
Post a Comment
Read more

Adventures of a Computational Explorer - Stephen Wolfram ***

Stephen Wolfram, the man behind the scientist's mathematical tool of choice, Mathematica, plus a whole host of other software products, including the uncanny Wolfram Alpha knowledge engine, is undoubtedly a genius of the first order. In this book, we get an uncensored excursion into the mind of genius - which is, without doubt, a fascinating prospect. The book consists of a collection of essays and speeches that Wolfram has produced over the last ten to fifteen years, covering an eclectic range of topics. Like all such collections, the result is something that lacks the coherence of a book with a narrative that runs through it, inevitably introducing a degree of repetition and a mix of interesting and not-so-interesting topics - but there's likely to be something to catch the attention anyone who is into computing or mathematics. One of the most interesting pieces is the opening one, where Wolfram describes being a consultant on the SF movie Arrival. He seems to hav...
Post a Comment
Read more