Writer, Poet -  and Mathematical Statistician

Click below for:
A PERSONAL HISTORY OF BAYESIAN STATISTICS, a history of my academic subject from
the 18th century to the current day, written with the help of my Bayesian friends around
the world, and my fellow creative writers and poets in Edinburgh.
8th January 2014: The first three chapters and part of the fourth chapter of my Bayesian history have been accepted for publication by John Wiley&Son of Chichester and New York for publication in their on-line library, and will instead appear there.
Please click on WILEY INTERDISCIPLINARY REVIEWS to access these chapters.
On 28th February 2014 Wiley honoured my Bayesian history by naming it their hot article
of the week. On 16th May 2014 they published a featured interview of me. Please click on
STATSLIFE for my online article about the history of Bayesian Statistics which was published by the Royal Statistical Society.
AN ANTHOLOGY OF SCOTTISH CONSCIOUSNESS for a collection of YouTube videos of
poems and aesthetic pieces of prose by the Leith Walk Rhymers and their invited guests.
THE EDINBURGH ALL-COMERS WRITERS CLUB, a convivial group which meets weekly
to encourage creative writers and poets of all abilities
A DEVONIAN SAGA, several sample chapters of my latest novel, a murder and family
ancestry mystery set during my teenage years in Plymouth.
HEALTH WARNING and my ongoing public health campaign (The Auntie Nancy campaign)
This month's  CORRESPONDENCE  about my health campaign
Stephen Sacco's MEDIA REPORTS for a pdf file containing numerous press reports concerning the harmful effects of psychiatric medications.
My PSYCHIATRIC HOME PAGE concerning my mental health campaign
NEWS FLASHES for some topical announcements
THE LIFE OF A BAYESIAN BOY, my academic life story
CHAPTER 5 OF BAYESIAN BOY for a discussion of the August 2013 ISBA-related debate about the axiomatic foundations of Bayesian Statistics, and a refutation of Birnbaum's 1962 justification of the Likelihood Principle.
The Martyrdom of CHEN WEN CHEN, Taiwanese hero and statistician
BEING DYSPRAXIC by Scott Forster
Please see my favourite Facebook quotations for some cryptic clues to some of the mysteries posed on this website.


 My favourite quotes by Catherine of Siena:
 "If you are what you should be, you will set the whole world on fire!"
 "Proclaim the truth and do not be silent through fear."
 "Every step of the way to heaven is heaven."
I  am  a  writer  of  fiction,  and  a  mathematical  and  interdisciplinary statistician, and I  was born  in  Yealmpton,  Devonshire  (the home of
Old Mother Hubbard)  and  live  in  Broughton,  Edinburgh,  Scotland,
where  witches  and  wizards  were  once  imprisoned in the tollbooth
before  they  were  burnt  at  the stake.  I  obtained my  degrees  from
Imperial College London  (in 1970)  and  University  College  London
(in 1971 and 1973), before embarking on an adventurous  academic career in England , the United States, and finally Scotland. 
I am a fellow of the  Royal  Statistical  Society  and  a  co-founder,  with Arnold Zellner, of the International Society for Bayesian Analysis (ISBA).
I also co-founded  the  Department of Statistics and MORSE degree at the University of Warwick with Robin Reed and P.J. Harrison.
In  December  2012,   the  ISBA  Board  (Fabrizio  Ruggeri  President) elected me as one of the first ever ISBA Fellows (to commemorate the 20th anniversary of the society) to honour me as one of  the founders of ISBA,  and for my outstanding contributions to  Statistics  (I devised the name  of  the  society  in 1992).   I  am  therefore  now  a  Fellow  of  the International Society for Bayesian Analysis. Thank you, Fabrizio!  In January 2014,  I enrolled as a member of SISbayes (Sonia Petrone, President), the recently formed Bayesian section of the Italian Statistical Society.
On 26th February 2014, I was elected to the Committee of the Edinburgh Section of the Royal Statistical Society. This is the best attended section of the Society outside London and is very influential throughout Scotland, It meets in the International Centre for Mathematical Sciences on South College Street.
Quite apart from my  academic duties. I was an accredited expert witness in the states of Wisconsin, Minnesota, Iowa and Illinois,  and I  also  enjoyed  visiting Santa  Barbara and San Francisco.  When I returned to Britain, the paper chase and the ripples from  above seemed to take over.


Tom Leonard, Arnold Zellner and other Bayesians attending the inaugural ISBA conference in the Hotel Nikko in San Francisco in 1993.
The four other Bayesians are Gordon Kaufmann, Wes Johnson,
Carl Morris and Shanti Gupta

Tom playing Rev. Thomas Bayes returning from Heaven
Valencia 6 Cabaret 1998. The Master of Ceremonies
Tony O'Hagan played ping pong with Tom at UCL

For further information about my academic career please google Tom Leonard Bayesian and Tom Leonard Statistician.
Please click here for a summary of my FAMILY ANCESTRY. I include a resolution of a historical controversy surrounding the 1892 Murders in Peter Tavy, which involves my presumed great grandfather Philip Hoskyns Bryant (See also Tavistock's Yesterday's, by Gerry Woodcock, Vol.8, Ch.9). The resolution is detailed in my father Cecil Leonard's 1979 account.
For my recently updated and illustrated academic story, please click here to read THE LIFE OF A BAYESIAN BOY.  A number of pivotal issues are raised which relate to the philosophy and history of Bayesian Statistics.
Click here for TONY O' HAGAN INTERVIEWS DENNIS LINDLEY for a recent discussion of the Bayesian paradigm by my former Ph.D. supervisor Dennis Lindley. My own philosophy is rather more pragmatic and I've always had very serious reservations concerning the relevance of the (paradoxical) Savage and (relatively tautologous when appropriately strengthened) De Finetti axiom systems. See Fishburn (Statistical Science 1986) for a discussion of the very complicated strong additivity and monotone continuity assumptions that need to be included in the De Finetti axioms to imply countable additivity of your subjective probability distribution. Please click on CH.5 BAYESIAN BOY for further discussion and developments.
On 5th September 2013, I felt honored, twelve years after my retirement from academia, to receive an invitation from John Wiley & Son to write a Short History of Bayesian Statistics, for electronic publication. This was after the American editors had read my somewhat controversial academic life story on this website, including the new material in Chapter 5. I will be preparing this relatively uncontroversial article during the next three months, while seeking advice and suggestions from fellow Bayesians around the world. It will be written from an American non-religious Bayesian perspective, and I hope that it doesn't irritate the British too much.


For the patient being diagnosed, let D denote the presence of a particular disease, and S denote the presence of a particular symptom. Furthermore, let p denote probability or chance. Then Bayes Theorem tells us that

                       p(D given S)= p(S given D) p(D)/P(S)

                      where p(S) = p(S given D) p(D) + P(S given ‘not D’) p(not D)

For example, if p(D)=prior probability of disease=0.1, p(S given D)= 0.99 and p(S given ‘not D’)=0.2, then

                     p(S)=0.99X0.1 + 0.2x0.9 = 0.279

                     p(D given S)=posterior probability of disease = 0.99X0.1/0.279= 0.355

Morever,     p(D given ‘not S’)= p(‘not S’ given D) P(D)/P(not S)=0.01X0.1/.721 = 0.0014

                      These formulae are essential tools in medical diagnosis.

See the book Bayesian Methods: An Analysis for Statisticians and Interdisciplinary Research Workers by Thomas Leonard and John S.J. Hsu (Cambridge University Press, 1999) for applications of more complicated versions of Bayes Theorem to a wide range of scientific, sociological and medical situations. For example, the correct version of Bayes Theorem in Criminal Cases, when there are a number of initially equally likely suspects, is described on page 78.

If N is the size of the entire population of suspects and there is no initial evidence to distinguish between the suspects then 'Laplace's Principle of Insufficient Reason' may be applied. This tells us that the prior probability that the defendant is guilty should be set equal to 1/N. Many courts erroneously set this prior probability to be equal to 1/2.

The preceding advice addresses one of the key issues in the ongoing DNA EVIDENCE CONTROVERSY. Please click here for further details.


Click here for:  George E.P. Box (1919-2013), A Wit, a Kind Man, and a Statistician  (back-browser to return)

Click on THE ACCIDENTAL STATISTICIAN to see Norman Draper's review of George's last book
A Statistics Department Faculty Skit
Madison, Wisconsin, Christmas, 1983
The participants are Richard Johnson, Grace Wahba, George Box, Tom Leonard, Tim Reed, and John Gurland
      My former Ph.D, supervisor Dennis V.Lindley (1923-2013) sadly passed away in Minehead, Somerset on 14th December 2013. He will be celebrated as a truly great teacher, and for his impact on generations of postgraduate students and on Bayesian Statistics. David Spiegelhalter, Phil Brown, Michael Goldstein, Nick Polson, Tony O'Hagan, John S.J.Hsu and Michael West are among his numerous academic descendents.

      By coincidence, Dennis died shortly after I had completed my Concise History of Bayesian Statistics. His best contributions included his 1958 refutation of Fiducial inference, his 1962 Bayes-Stein estimator for several normal means and his 1964 Bayesian Analysis of Contingency Tables. He is however longest remembered for his absolutely seminal work on queuing theory which he developed while an assistant lecturer at the University of Cambridge in 1950.

      Dennis was later Professor and Head of Statistics at the University College of Wales, Aberystwyth and University College London, His wife Joan is a cousin of the statistician Peter Armitage, and a beautiful and kindly lady.

      Please Click on  REVERB DENNIS LINDLEY for a variety of articles relating to Dennis's academic career.

Tom's literary advisor Eystein Thanisch

While I have published two scientific books, and numerous articles in international  journals, I write fiction primarily for fun. I am an active member of the Edinburgh All Comer's Writers Club, which meets in Sofi's Bar, Leith from 7 till 10 pm on Tuesday evenings.

Click below for free access to my poems, short stories and novels.


To contact me on a non-trivial issue,  e-mail me on

THE EDINBURGH ALL-COMERS WRITERS CLUB meets in the cosy backroom of Sofi's Bar (63-65 Henderson St, Leith) every Tuesday at 7 pm. Please visit our Facebook page for on-line information and new announcements.
Are you interested in attending an Edinburgh Writers club? Then come to the highly creative Edinburgh All Comers Writers Club. the most convivial and laid back creative writers club in Edinburgh! Please feel free to attend even if you have just scribbled your first short story or poem on the back of an envelope.

Read your piece of prose or your poem to the group, or just join in the stimulating discussion and multi-faceted conversation, which are uniquely designed to be both gentle and constructive on criticism. Our grass-roots, democratic group is all-accepting, non-phobic, and follows a safe-space policy, and our hosts in Sofi's Bar are very welcoming and hospitable. We are one of the most successfully-published creative writers groups in Scotland, and our members include the highly original, socially aware Scottish poets James Carter and Scott Forster, the talented budding playwright Neil Chue Hong, the dynamic creative writer Colin Reid, Steve the Boxer, who read his first poem to us in January 2014, and several undergraduates and Masters students.
My other pastimes include chess (when I played in tournaments the highest
international  rating  I  was able to  achieve  was 2150.  I once defeated the Russian Grandmaster Roman Levit and I  have  drawn  with  Grandmasters
Colin McNab and Mark Hebden as well as losing  to  far  too  many  school
kids), sending presents to my three grandchildren in England and to my six
great  nephews  and  nieces,  history,   and  non-judgemental  religion  and spirituality.
On 18th May 2013 I beat an international player rated 1888 on
After over 600  blitz  games  in  three  months,  my  rating  has
therefore risen to 1720. Let's go for it!  2150, here we come.
On 1st  October  2013,  I  put  my  opponent  in  checkmate  at  2.15 am  to
achieve  a rating of 1801, after 1061 wins, 608 losses and 97
draws while playing 10 minutes blitz over a period of several months.  I am advised that ratings are about 200 points less than Scottish or
FIDE ratings. This therefore appears to be equivalent  to a  FIDE rating  of  about  2001.  Whoopee! In the US that would make me an expert.
I once fled  in  horror  from  a  fundamentalist  Evangelical  Free  Church  in
America where I was a Sunday School teacher, but where faith was valued
much   more  highly   than  good  deeds,   and  charity   was  only  shown  to
selected  Christians.   Some  of   the  more-accepting  churches  in  Britain
spread  the  word   much   more   impressively,   but   can   be   surprisingly
demanding and all-controlling in fiscal terms. For example, restoration and improvement funds  sometimes  take  precedence  over  more  than  token

The Toadstool Ring in Hopetoun Crescent Gardens.
(See Chapter 4 of my Calton Hill novel)

I occasionally try to promote the interests of our gay,  lesbian and transgender communities  (as inspired by my December 1989  speech against  gay  discrimination in the military in Madison, Wisconsin  that appears, in hindsight, to have created substantial  social impact. I was drawn into this controversy when a U.S. army captain advised me, at an otherwise convivial faculty reception,  that ‘these freaks have never even opened a bible.’)
For informal advice on LGBT issues, click here for Gay Euclid Edinburgh.


Tom with his friend Kingsley from Adelaide (October 2012). Soon after
this photo was taken, Kingsley moved south to work near London, but he and Tom are still in touch.
  Tom and his friend Thomas at a the Jack Jones farewell concert in the Usher Hall, Edinburgh, on 22nd May 2013.
Thomas and I exchanged bracelets on 26th July 2013 to celebrate our platonic friendship. We first met on 25th March 2012 in Edinburgh. Please click here for PICTURE.


Tom's Polish-American friend Nikolai (Nicola) Romanski

The Scottish poet Scott Forster

Tom's friend Alan

22nd July 2013 Congratulations Nicola!

Nicola finally arrived in Janesville, Wisconsin today after an adventurous journey from West Hollywood where she'd composed the poem 'The Thaw and the Revival' with me via Facebook. She is now living with her sister Wanda after a lengthy absence on the West Coast. Nicola and I met in Madison, Wisconsin in 1988. Good luck, Nicola!


Euclid of Alexandria, Greek Mathematician and Philosopher
Returning from Heaven


Tom Leonard aged 38

Tom aged 19   Tom aged 28
  © Thomas Hoskyns Leonard, 2012 - 2015