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  {\Large\textbf{The Reverend Thomas Bayes, F.R.S. --- 1701?-1761}} \\

  {\large\textbf{Who Is this gentleman? When and where was he born? }}
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\noindent
The first correct (or most plausible) answer received in the Bulletin
Editorial office in Montreal will win a prize! 

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\noindent This challenge was made in \textit{The IMS Bulletin},
Vol.\,\textbf{17}, No.\,1, January/February 1988, page 49.  The
photograph is reproduced, with permission, from the page facing December
of the \textit{Springer Statistics Calendar 1981} by Stephen M.\ Stigler
(pub.\ Springer-Verlag, New  York, 1980).  It is noted there that ``the
date of his birth is not known: Bayes's posterior is better known than
his prior.  This is the only known portrait of him; it is taken from the
1936 History of Life Insurance (by Terence O'Donnell, American
Conservation Co., Chicago).  As no source is given, the authenticity of
even this portrait is open to question''.  The original source of this
photograph still remains unknown.  The photo appears on page 335 with
the caption ``Rev.\ T.\ Bayes: Improver of the Columnar Method developed
by Barrett.  [There is a photo of George Barrett (1752-1821) on the
facing page 334: ``Mathematical genius and originator of Commutation
Tables: Ignored by the august Royal Society in its \textit{Transactions}
because he had never gone to school.'' -- See also comments by Stephen
M.\ Stigler on page 278.] 

\medskip

The most plausible answer received in the Bulletin Editorial office is
from Professor David R.\ Bellhouse, University of Western Ontario,
London, Ontario, Canada.  A prize is on its way to  Professor Bellhouse,
who wrote: 

\medskip

\noindent
``The picture in \textit{The IMS Bulletin} is supposedly of Thomas
Bayes, who died in 1761 aged 59 and so was born in 1701 or 1702.  I have
added ``supposedly'' since I believe that the picture is of doubtful
authenticity.  There are three clues in the picture which lead me to
this conclusion.  For the purpose of comparison, consider the pictures
(below) of three other Nonconformist ministers: on the left Joshua
Bayes, Thomas's father (d.\ 1746); in the middle Richard Price (this
portrait is dated 1776), who read Bayes's paper before the Royal
Society; and on the right Philip Doddridge (1702--1751), who was a
friend of Bayes's brother-in-law, Thomas Cotton. 

``The first thing to note in this picture is the apparent absence of a
wig, or if a wig is present, it is definitely the wrong style for the
period.  It is likely that Bayes would have worn a wig similar to
Doddridge's, which was going out of fashion in the 1740s, or a wig
similar to Price's, which was coming into style at the same time.  The
second thing to note is that Bayes appears to be wearing a clerical gown
like his father or a larger frock coat with a high collar.  On viewing
the other two pictures, we can see that the gown is not in style for
Bayes's generation and the frock coat with a large collar is definitely
anachronistic.  Finally, Price is wearing a stock or wide collar on his
shirt which appears around his neck in the picture; this was fashionable
from about 1730 to 1770.  Since Doddridge, one generation younger,
appears without any stock or shirt collar, it is questionable whether
Bayes would have worn a stock.  However, the nineteenth century-looking
clerical collar in this picture is again anachronistic.  For reference,
I have used C.\ Willett Cunnington and P.\ Cunnington, \textit{Handbook
of English Costume in the Eighteenth Century}, pub.\ Faber \&amp; Faber,
London, 1964. 

``It may be impossible to determine Thomas Bayes's exact date of birth.
All that is known is that he died on 7 April 1761, at the age of 59.
That is what is recorded on his tomb in Bunhill Fields in London.  It
also corresponds to his death notices in three eighteenth century
periodicals -- \textit{Gentlemen's Magazine}, \textit{The Public
Advertiser}, and the \textit{Whitehall Evening Post}.  I might add that
the date of death has been erroneously given as 17 April in several
places (e.g., \textit{The History of Statistics: The Measurement of
Uncertainty before 1900} by Stephen M.\ Stigler, pub.\ Harvard Univ.\
Press, 1986, page 971 going back to at least the mid-nineteenth century.


``The inscription on the front of the tomb (as illustrated) reads:
``Vault of the families of Bayes and Cotton.  Thomas Bayes Cotton, son of
Bayes Cotton and Sarah, his wife, and great grandson of the said Joshua
and Ann Bayes (10).\ 21 March 1787.''  On the top of the tomb is
inscribed: ``Rev.\ Thomas Bayes, Son of the said Joshua and Ann Bayes
(59).\ 7 April 1761.  In recognition of Thomas Bayes's important work in
probability.  The vault was restored in 1969 with contributions received
from statisticians throughout the world.''

``Before the calendar reform of 1752, the English New Year was on March
25.  So -- Bayes died on 7 April 1761: subtract the 11 lost days for the
reform of 1752 which makes his death date in the old style as March 27
or two days after the new year.  Now subtract his age (59).  Since the
year 1701 occurred from March 25 of 1701 (new style) to March 24 of 1702
(new style) then it is almost certain that the year of his birth would
have been recorded, if it has been recorded at all, as 1701. 

``It was reported by J.D.\ Holland [\textit{J.\ Roy.\ Statist.\ Soc.\
Ser.\ \textbf{A}} \textbf{125} (1962): 451--461] that he searched for
Bayes's birth date in the parish registers of Bovingdon, Hemel
Hempstead, Hertfordshire, Bayes's most likely place of birth.  He also
reported that the parish registers and bishop's transcripts of the
registers were missing for the period 1700--1706 so that a birth date
could not be fixed.  I believe that Holland was looking in the wrong
place.  I checked the International Genealogical Index (IGI) compiled by
the Church of Jesus Christ of Latter Day Saints (Mormons) and found no
children of Joshua Bayes listed even after the family's move to
Southwark and London.  This leads me to believe that all the children of
Joshua Bayes were baptized in the dissenting chapel, not in the
established church.  I am currently trying to find the Nonconformist
registers that would most likely contain Thomas Bayes's baptismal
record.  It is unlikely that anything will come of this search since
many early Nonconformist registers have not survived.  That is the most
likely explanation for the lack of Bayes children appearing in the IGI
indexed by the Mormons.  I will let you know if anything comes of this
search. 

``I have done some further investigation of Bayes.  I have found a
genealogy of his family and a related family, the Cottons.  No birth date
is given for Thomas but there may be some clue to where one might find a
picture of him.  The genealogy states that the Cotton family possessed
some portraits of members of another family which was related to them.
Also, a descendant of Joshua Bayes's son-in-law, Thomas Cotton, was an
attorney-clerk to the Williams Library.  That is probably how Joshua
Bayes's picture wound up in this library.  If they had a picture of
Thomas, it may have been kept in the family, since Thomas Cotton's son
was named Thomas Bayes Cotton.  Tracing a picture of Thomas Bayes then
requires hunting down the descendants of the Cottons, a difficult but
not an impossible task.''

\bigskip

\noindent
We also received a letter from Professor Andrew I.\ Dale, University of
Natal, Durban, South Africa, who noted that the photo is in the book by
O'Donnell (1936), Professor Dale also observed that: 

\medskip

``While the style of dress as shown in the picture is not atypical of
that of a nonconformist minister of the 18th century, there is no   
reason to suppose that it is in fact a portrait of the illustrious
Bayes.  O'Donnell's book, as he states in the preface, is ``a plethora
of rare and curious old illustrations'', and no reference to the source
of the photograph is provided.  Moreover, the reference to insurance
sheds further doubt   on the ascription.  O'Donnell is elsewhere
unreliable.  For example, he refers to the author of ``An Essay on
Probabilities and their Application to Life Contingencies and Insurance
Offices'' as William de Morgan (who was in fact Augustus's son).  The
reference is, however, correctly attributed in the Bibliography.''

\bigskip

\noindent
As we go to press (20 May 1988) we received these comments from
Professor Stephen M.\ Stigler, University of Chicago, USA. 

\medskip

``George Barrett (1752--1821) was an actuary who prepared a series of
life tables for the Hope Life Office around 1813.  He came from
Petworth Sussex, and is usually considered the originator in England of
the method of calculating the values of annuities by means of a
commutation table, a method sometimes called Barrett's columnar method.
The method was apparently developed between 1788 and 1811, explained to
Francis Baily in 1811, and read to the Royal Society by Baily in 1812.
If Bayes improved the method before his death in 1761, he was indeed
precocious.  It could be noted that inaccuracies in O'Donnell's captions
do not necessarily invalidate the picture.  It still seems likely that
O'Donnell got the picture from some (perhaps 19th century) source where
it was identified as Bayes.  The question would then be: ``What is that
source, and what was that source's source?'' So little is said of Bayes
in O'Donnell's book that it is extremely implausible that he would
choose him (and Thomas Simpson, who is also depicted in a similar style)
as the subject for an invented picture.''

\textit{Many thanks} to Professors Bellhouse, Dale, and Stigler for
their comments.  The \textit{Bulletin} Editor would like to draw our
readers' attention to the Wald Memorial Lectures to be given this year
at the IMS Annual Meeting in Fort Collins, Colorado.  As noted on page
189 of this issue of the \textit{Bulletin} these lectures will be given
this year by Professor Dennis V.\ Lindley (Minehead, Somerset, England)
on ``The present position in Bayesian statistics''. 

\medskip

\begin{flushright}
  \textit{The IMS Bulletin}, Vol.\,\textbf{17} (1988), No.\,3, pp.\,276--278.
\end{flushright}

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