The Life and Work of Thomas Bayes

-The Life and Work of Thomas Bayes-


    I find it impossible to write a preface to this work, without discovering a little of the enthusiasm which I have contracted from an attention to it.
    Joseph Priestley.
    The History and Present State of Electricity.

It is generally considered bad form in writing, unless on matters autobiographic, to make unbridled use of the perpendicular pronoun. The reader of the present book, however, may well wonder why one would want to study the life and works of Thomas Bayes, ‘this strangely neglected topic’(1), and it is only by a reluctant use of the first person singular on the part of the author that this legitimate question can be answered.

It was in the late 1960s that my interest in various aspects of subjective probability was awakened by some of the papers of I.J. (‘Jack’) Good, and this was followed by the reading of works such as Harold Jeffreys’s Theory of Probability. In many of these the (apparently simple) result known as Bayes’s Theorem played a pivotal role, and it struck me that it might be to satisfy this curiosity in spasmodic periods over many years I discovered that little information seemed to be available. Writings by John D. Holland in the 1960s shed some light on the matter, but it was only in periods of sabbatical leave that I was able to undertake the intensive (and extensive) archival research needed to flesh out the shadowy figure after whom one of the major branches of modern statistics is named.

Where, for instance, was Bayes educated? The answer to this question presented itself by chance to me when I was visiting the University of Chicago. While waiting for some rare volumes to be retrieved from the depths of the John Crerar Library in which there appeared details of a certificate recording the admission of Thomas Bayes as a student. Visits to Edinburgh and the generous co-operation of the library staff resulted in the finding of a number of references to Bayes in the archives of the University.

Similar serendipity led to my finding of the proof, written mainly in Latin, of one of the rules in Bayes’s Essay towards solving a Problem in the Doctrine of Chances in a Notebook attributed to him and held in the Equitable Life Assurance Society in England. This not only reinforced the opinion that the Notebook was indeed written in Bayes’s hand, but also shed light on matters that Bayes had thought worth recording.

Once the question of Bayes’s education had been solved, or at least answered to the best of my ability, it seemed necessary to investigate his family and life in Tunbridge Wells, where he spent many years as Presbyterian minister. Although some information on these matters was available from (fairly) modern writings, it seemed expedient rather to consult writers as near to Bayes as possible, and in doing so, of course, I was merely quarto edition of his Decline and Fall of the Roman Empire, stressed that he had made it his earnest endeavour always to consult the original sources. Perhaps Gibbon, in his turn, was following the example set by Watson in his edition of The Works of Horace:

    Whoever attempts, at this distance of time, to write upon a Classic, ought nit only to read over what the most approved commentators have written upon his works, but to compare the same carefully with the text itself; otherwise he is in danger of being misled: for many of them, instead of illustrating, only darken their author, and palpably mistake his meaning.
    [1792, p. v]

There are three eighteenth-century savants who are known to modern statisticians and historians of statistics and historians of statistics for single contributions(2): Thomas Bayes, Roger Boscovich(3) and Thomas Simpson(4). Bayes is known for his Theorem, published in his posthumous Essay in 1764, Simpson for his work in 1755 (extended in 1757) on error distribution, and Boscovich for the posing of a question in 1757 (and its solution in 1760) on the fitting of a straight line to observational data(5). Boscovich and Simpson have both been the subject if biographies(6), and it seems not inappropriate that Bayes be similarly commemorated, particularly as the tercentenary of his birth is upon us.

In drawing to a conclusion let me say a brief word about the presentation of material here. As regards the method of citation, works such as Bayes’s Essay towards solving a Problem in the Doctrine of Chances, published in the Philosophical Transactions in 1764 in the volume for 1763, are cited as ‘Bayes [1763]’. If a word in the original broken across two pages, [n] appears here at the end of the word, with broken formulae being similarly treated. Footnotes are given in the usual way, irrespective of how they may be positioned (e.g., broken over two pages) in the original. Things that appear in crotchets, […], are my corrections or additions, even in exponents in formulae. In giving Bayes’s tracts I have allowed myself the liberty of a light editing. In the Essay, for example, what appear in much mistaken’ and ‘in nature’, and ‘(a+b)b+q’ in the first paragraph of much mistaken’ and ‘in nature’, and ‘(a+b)p+q’. On page [400] the last occurrence of 2Eapbq appears in the original as 2Eapbq, and the second ∑ on page [416] appeared originally as E. No changes are more serious than these and all would easily be made by the reader of the original texts.

Not being an expert in eighteenth-century history, I must bring to this study a certain naivete, a quality that I hope will be seen by the reader as touching rather than irritating and obtrusive. There are no doubt portions of this work that could be better handled by a historian; but one of the results of approaching a topic in ignorance is the pleasure of discovery(7), with in this journey through Bayes and other coves that certain passages – for example the remarks on the Great Plague and the descriptions of Tunbridge Wells – are presented.

    He could not butt feel that, like an eminently aristocratic family cheese, it was much too large for his wants, and bred an infinite amount of parasites.

Rather, as George Berkely put it in Siris: a Chain of Philosophical Reflexions and Inquiries:

The displeasures of some readers may perhaps be incurred by surprising them into certain reflections and inquiries for which they have no curiosity. But oerhaps some others may be pleased to find a dry subject varied by digressions, traced through remote inferences, and carried into ancient times. [350]

Durban, Natal, Andrew I. Dale
South Africa

1. See Kingsley Amis’s Lucky Jim, [1954, chap.1].
2.See Stigler [1984].
3. For various forms of Boscovich’s Christian names see Farebrother [1999, 2.5].
4.See Stigler [1984] for future details.
5. For a detailed study of the calculus of observations see Farebrother [1999].
6. See Clarke [1929] and Whyte [1961].
7. See Lynd [1928, p.2].
8. Charles Dickens, Our Mutual Friend, vol. I, Book II, chap. VIII