Bayes' theorem, sometimes described as the theorem of inverse probabilities for finding the probabilities of the different causes any one of which could have led to an observed effect, is justly famous as one of the key pillars of modern statistics — in particular for the way it allows the incorporation of subjective probabilities into such computations without relying only on frequency-based probabilities. Moreover, the field of Artificial Intelligence has found further valuable uses not envisaged by the Reverend Bayes in the 18th century, and Bayesian Artificial Intelligence has become a rapidly expanding field. But there has been no comprehensive study of the life and works of the author of the theorem. In his preface to Most Honourable Remembrance, Andrew Dale explains that his aim was to "flesh out the shadowy figure after whom one of the major branches of modern statistics is named".
The extensive and careful work which the author has put in to achieve his aim is evident everywhere in the book. It must obviously have involved a lot of labor — evidently a labor of love for the author — to collect all the details he has given about Thomas Bayes' ancestors, his early schooling and life, the town he lived in, the burial ground he was buried in, the inscriptions in the burial ground, the will Bayes left, and so on. It is all there in as much detail as anyone could ask for.
Interesting and useful as all this will be for anyone interested in knowing more about Bayes, this is just part of the riches contained in this book. The seminal essay on The Doctrine of Chances in which Bayes first propounded his views is printed in full, with a an introduction and an illuminating commentary placing the paper in context and relating it to the views of other founders of probability theory such as Bernoulli and Laplace. The commentary also explains how in addition to the famous Bayes theorem, the paper also contains contributions to pure mathematics in relation to issues like the evaluation of the incomplete beta function. Furthermore, Dale provides similar introductions and commentaries for the other lesser-known (one might better say hardly-known) works of Bayes, such as his Introduction to the Doctrine of Fluxions, in which he provided counter-arguments against Bishop Berkeley's criticism of calculus, or his theological paper on Divine Benevolence, and his writings on a miscellany of subjects including electricity and celestial mechanics.
One emerges from the book with two feelings: first, that Bayes was one of the most powerful thinkers of his time and that to think of him only in terms of Bayes' theorem is to do him less than justice; second, that Dale has not just "fleshed out the shadowy figure " of Bayes, he has done much more by his careful and deep analysis of Bayes work as a whole. Beyond doubt this book is a work of the highest quality in terms of the scholarship it displays, and should be regarded as a must for every mathematical library.
Ramachandran Bharath is Visiting Professor of Mathematics at Colby College.