The Life of a Bayesian Boy

Tom Leonard
CDC Section: Contributions, Discussion and Corrections

Please submit your contributions to:  They may be lightly edited.

(1) My joint work with Mohammed Madi
(2) Applications in Astronomy
(3) Chong Gu’s contributions to density estimation
(4) Jim Albert’s publications
(5) My 1978 ICL lecture notes on Bayesian categorical data analysis
(6) Caroline Robinson’s research on Bayesian template modelling
(7) My undergraduate vacation work (1969 and 1970)
(8) Orestis’ STATLAB report
(9) A key reference in Astrophysics
(10) HEALTH WARNING appeal (Epilim Crono and other physically damaging mind control medications)
(11) The international response to Bayesian Boy
(12) The Statistics Group at the University of Edinburgh
(13) The DNA Evidence Controversy
(14) The Madison AIDS/HIV data
(15) Sales of Bayesian Methods (1999, with John Hsu)
(16) The Higgs Boson and the Hadron Collider (ISBA and Tony O'Hagan)
(17) Advice to Abbott Laboratories of Wiesbaden
(18) E-mail from Orestis Papasouliotos (Merck Group)
(19) The real winner in the US elections: Thomas Bayes
(20) Tom is honoured by ISBA
(21) Greetings from Tom's erstwhile 709/710 student, Professor Neil Gandal, University of Tel Aviv
HEALTH  WARNING  appeal   DNA  Evidence  Controversy
1)  I published two joint papers with Mohamed Madi. One was on Bayes inference for the location parameters of several exponential distributions. The other concerned simultaneous inference when there is a degree of uncertainty about the parameter constraints. The second was co-authored with Mohamed’s Ph.D. supervisor Kam Wah Tsui.

2)  Applications in Astronomy: In 1996, Orestis and I advised a couple of University of Edinburgh astronomers (whose names I do not recall), on behalf of our STATLAB, regarding the analysis of their ‘ionising flux in redshifts’ data. Owing to the complexity of their model, we developed Tierney and Kadane Laplacian approximations to the marginal posterior densities of their parameters of interest. They acknowledged our contributions in their paper, and our approach seems to have since spawned a cottage industry in Astronomy.

Does anybody know who the original co-authors were?


3)  I haven’t given enough credit to Grace Wahba’s former Ph.D. student Chong Gu. During the 1990’s Chong published a series of
papers that used non-linear smoothing splines to extend and generalise my JRSSB 1978 density estimation method (that assumed a Gaussian prior process for the logistic density transform).

Chong also did something elegant, useful, and hot off the press with the Leonard-Hsu-Tsui JASA1989 generalised Laplacian approximation, as did Wing Wong. Thank you for giving me so much credit! Chong, whose a likeable lad, has since pursued an eminent career at Purdue.

4)  I haven’t credited Jim Albert’s fine publications on Bayesian categorical data analysis and item response theory, some of which
referred to my previous work. He was one of Jim Berger’s most prolific students, and that’s saying something.
5)  In 1978, David Cox invited me to return to Imperial College to give a short course to his Masters students on Bayesian categorical data analysis, exactly ten years after I’d flunked there as an undergraduate. Argentina beat Peru six nil in the World Cup on my arrival. My lecture notes were circulated more broadly e.g. at the 1979 Gregynog conference. In 1980 they helped me to secure my tenure case in dramatic style at the University of Wisconsin-Madison.
6)  In about 2000, Caroline Robinson graduated with a Ph.D. in Statistics at Edinburgh. She’d developed a Bayesian template technique for BIOSS and the Roslin Institute for estimating the amounts of meat in sheep. STATLAB advised her how to do this.

Heaven knows who took the credit.

7)  It is worth supplementing my account of my undergraduate career, by saying that during the summer of 1969 I worked in the
claims department of the Clerical and Medical insurance company grinding out surrender values on a Brunsweiger calculating
machine. I survived with my wife in our bedsit in Onslow Gardens on £8 a week, and visited the City each day in a smartly pressed

           Just three years later, I told Jim Hickman in Iowa City about my Bayesian histogram smoothing method, and this preceded
his and Bob Miller’s contributions to the actuarial graduation literature.

           I spent the summer of 1970 working for the Metal Box Company in West London for £16 a week. I firstly developed a method
for optimizing the dimensions of a cardboard box with a liner. This led to my first ever publication, an internal report co-authored
with Bob Armstrong. It was, however, my first ever experience of plagiarism. Bob, who died shortly afterwards, took most of the
credit. My colleagues in Madison were later amused by that story.

           For my second project with the Metal Box Company, I developed a least squares routine for a complicated non-linear
regression model for the analysis of chemical data. I however ran into all sorts of problems concerning the validity of the prescribed
model in regions of the sample space away from the data points and all sorts of related politics.


8)  E-mail Message from   2nd. May 2012

                                           Abbreviated, slightly edited, and occasionally paraphrased

Hi Professor Leonard,

           Please find some relevant information,

The Scottish Offender Neuropsychological Test Data. The information I have from the study by Ton Busuttil and Keith Ashcroft (from my Ph.D.thesis): The research was motivated by a study of the scores of five different groups of people (three kinds of offenders in Scottish prisons and two kinds of control from Stanford) on twelve neuropsychological tests. The main question of interest was whether different groups were associated with higher scores for certain tests. These tests were also thought to be related to participants in the study age.

           I applied practical and MCMC Bayesian techniques for my heterogeneous variance ANOVA model to the analysis of this
data set.


(a)    n=67 Stanford students

(b)   n=22 Scottish rapists

(c)    n=40 Scottish paedophiles

(d)   n=20 Scottish murderers

(e)   n=128 Stanford medical patients

           I began with a comprehensive analysis of the visual functions neuropsychological test.

           My general single covariate random effects model provided a major improvement to previous standard ANCOVA models used for these data, as the unequal variance assumption proved to be valid.

           From a practical viewpoint the obtained results provided a major surprise. Contrary to the expectations of our forensic pathology collaborators, who anticipated higher scores corresponding to more pathological conditions for the two sex offender groups, the mean score of the Stanford medical patient group was the highest, though not usually significantly higher compared to the scores of some of the offender groups, for eight out of twelve available tests.

           For the remaining four tests, their mean scores weren’t significantly different from most of the offender groups. Hence our data-analytic results certified that, at least using a single response and age as the only covariate, discriminating between the different groups was impossible.

           Therefore, we do not believe that neuropsychological test scores can be used to predict offender type, with the obvious implications.

           This work was published by Leonard and Papasouliotis (2002) in the Encyclopedia of Environmetrics. [ Thanks, Orestis. I never knew that!]

           The theoretical developments of the Bayesian analysis of my unequal variances random effects ANCOVA model are described in the first four chapters of my thesis together with the preceding forensic study. The fifth chapter is devoted to our development with Ian Main and Kes Heffer from BP of an algorithm for detecting the most productive pairings of injector and producer wells in hydrocarbon reservoirs. My external examiner was Dr. David Wright of the University of Plymouth. [ So Orestis published four papers out of his thesis with at least two more spinoffs]

           My other publications with STATLAB

           We must have completed well over a hundred projects between 1996 and 2000 while you were director (John Duffy took over
shortly before your retirement), and we were acknowledged by a number of Edinburgh researchers. I for example remember using
Bayes-Stein shrinkage estimators to smooth the graduate intakes to the Edinburgh Law School. [This paragraph is paraphrased—

           We published three joint papers with Ian Main and his geological co-authors in the geophysics journals. The two of us co-
authored the fourth chapter of your 1999 book on Categorical Data Analysis. It was entitled ‘The Madison Drug and Alcohol Abuse
’. This complemented three joint papers in family medicine journals on the same topic, with Richard Brown and Laura

           I published a joint paper with Bruce Worton et al in the Journal of Glaucoma (2003) on the quality of life in glaucoma and its
relation to visual function, and we published a joint Bayesian paper in the Journal of Cell Science with Nick Read et al.

           Our analysis of the Lepenski Vir Mesolithic and Neolithic skeleton data with Clive Bonsall et al does not appear to have been
published. I don’t have any record about the Bayesian work in Astronomy on ionising fluxes in high redshifts, to which you refer.

           My joint research on glaucoma with Bruce Worton et al was reported in three conference presentations. The abstracts
appeared in the Proceedings of the 19 th. and 20 th. Annual Meetings of the Glaucoma Society (1998 and 1999) and the
Proceedings of the Eighth Visual Field Symposium of the International Perimetric Society (1998)

I hope that everything is fine with you in Edinburgh,

Best wishes,   Orestis.

9)  12th May 2012: I've finally been able to track down the paper in Astophysics that employed Tierney-Kadane Laplacian approximations, at STATLAB's advice. The reference is Cooke, A.J., Espey,B. and Carswell, R.F. (MNRAS, 1997) Evolution of
ionizing flux in high redshifts.

Andrew Cook, who was responsible for the Statistics, was a researcher in the Institute of Astronomy at the University of Edinburgh. Brian Espey, who visited Edinburgh from the US in 1996, is now a Professor of Astrophysics at Trinity College Dublin.

10)  HEALTH WARNING:  A call for help to Bayesians everywhere.

(Psychiatric medications with severe physical side effects)


Please take up the cudgel!


Granville Tunnicliffe-Wilson has contacted me from the University of Lancaster expressing his concern at the HEALTH WARNING
and related discussion and correspondence that is described elsewhere on this website. He for example feels that the international pharmaceutical companies are not behaving responsibly enough in regard to psychiatric medications [e.g. Epilim Chrono and various anti-psychotic drugs] with debilitating side effects, and the introduction of possibly less harmful, e.g. holistic, treatments. My communications with a senior statistician working in a top pharmaceutical company suggest that Granville is right.

         Note that, while the medications for many physical ailments also come with physical side effects, mentally disabled people are seldom sufficiently cognisant to be able to adequately defend their interests. They therefore often find themselves in particularly vulnerable situations.

         When I recovered, in October 2011, from my six months of somnolence, lack of mobility, only a modicum of cognition, and two surgeries for cancerous melanoma after finally refusing to take my Epilim Chrono and being threatened with Carbamazine following ten years in a biochemical straightjacket, I started a local campaign against the Midlothian shrinks.

         I also heard from a friend who I will refer to as ‘Alexander’, a very pleasant and highly intelligent young man with an HNC who is now 34. Alexander said that he’d been paralysed from the waist down in 2001, and put in crutches after being forcibly injected with depixel (fluminpixel) by a pre-eminent shrink. He’d been sectioned by the police for thinking that he was Jesus, and performing a harmless prank. He was incarcerated in the Royal Ed for five and a half months, including fifteen days in a barred cell in solitary where he was arm-twisted by the orderlies. After that, he was painfully injected in his posterior with various other mind drugs, and kept taking it there ad nausaeum.

         As predicted by one of the medico-legal experts I consulted, my well-grounded complaints against NHS Mental Health Services Lothian hit a brick wall. Rather than going through the angst of complaining to the Ombudsman, I therefore decided to take my campaign to my website. What I have to say complements what the prestigious American Journal of Psychiatry says on these issues. Googling ‘Health Warning, Epilim Crono’ is also highly illuminating.

         I thought that I would initially press these issues through the LGBT Community, since bipolar disorder is more prevalent there. Many gay people with mood swings are certainly getting physically assaulted by their shrinks, even though some of their symptoms may have been misjudged in the context of the group craziness of portions of the gay community.

         It would be extremely dangerous to advise a friend or relative with schizophrenia to stop taking his or her mind drugs, because his mental illness could reappear in its full severity. Psychotic patients, or those experiencing highs, may be being injected with modecate or even depixel (fluminpixol). These have to be painfully injected, in the rear muscles, with horrible and frequently occurring side effects.

         If one of your friends or relatives is on mind drugs, then you should perhaps research the potential side effects of his medication on Google. Unfortunately, many of the frequently-occurring side effects are unlisted, including potential old age effects such as dementia and Alzheimer’s, and discussions with other patients are also illuminating. You should then try to judge whether the benefits of the drug outweigh the disadvantages of the side effects. Consulting a private shrink might help, but don’t believe any of them. Many of them also work for the NHS.

         I am doing my level best to pursue these issues. Perhaps Bayesians with more resources could now take up the cudgel. My friend Alexander would certainly appreciate that. He is still getting punctured in his posterior after eleven or more years of cruel mistreatments. And he’s perfectly innocuous.

         Who are these people, who dare to do these things to our kith and kin?  Lionel and I have compared notes, and our conclusions are not altogether dissimilar. Maybe the Chief Nurse at the Royal Ed, or the Professor of Public Health at Edinburgh University, should investigate. I publicly call upon them to do so.


Correspondence about Psychiatric Medications, and Related Developments


Return to Tom's Home Page



         During the 24 hours or so after I started circulating information about Bayesian Boy to statisticians around the world, on 11th May 2012, I was overwhelmed by the enthusiastic response. People e-mailing me included:


(a) Charlie Lewis (Fordham University and ETS): Nice to hear from you, forty years later, Charlie! Charlie is now Professor of Psychology at Fordham University, and the presidential representative to ETS regarding the fairness and validity of educational testing in the U.S.

         As reported in Bayesian Boy, I helped Professor Lewis to get tenure at Illinois in 1972, while I was a postgraduate student visiting ACT in Iowa City. Despite my own U-shaped career, I seem to be well-versed at helping other people to fulfil their ambitions.

         Charlie said that he’d forward my message to Ming-Mei Wang. She was my college at the Lindquist School of Measurement in Iowa City in 1984, and she’s now a Principal Investigator at ETS. Whatever happened to Shin Ichi Makewaya, Ming-Mei? And did I ever get to co-author our Empirical Bayes approach to Factor Analysis, which presumably appeared in his thesis?

         During our friendly interchange, Charlie and I developed the philosophy,

                                        ‘Bayesians never die, but their data analyses go on before them’

(b) Norman Draper and Murray Clayton (University of Wisconsin)

         It was good to receive two tokens of approval from my former department in Wisconsin. Norman (or Mr. Regression) is now the doyen of the Department of Statistics there. I wish you many years of similarly fruitful retirement, Norman! You once put down ridge regression in the sound and capable fashion it so thoroughly deserved.

         Murray has an outstanding Bayesian pedigree. His Ph.D. advisor was Don Berry at Minnesota, and Don’s advisors were L.J. Savage and Jay Kadane. Murray has consequently published many prestigious contributions to Bayesian inference. He has also consulted extensively in the UW Ag School and risen high in the University hierarchy.

(c) Norman Fenton (Queen Mary College London). Norman e-mailed me seeking more information relating to my objections to alleged probabilities of guilt based upon DNA evidence, and for a rundown on the forensic scientists and statisticians involved. My response to him, and my e-mails to Peter Donnelly and David Balding, are discussed in item 13.

(d) Mike Evans (University of Toronto). It was good to hear from Mike that I’d already met him while I was visiting Irwin Guttman, and that he was therefore already my friend. Mike wrote an encouraging and frequently-cited review on my 1999 CUP book with John Hsu, Bayesian Methods, An Analysis for Statisticians and Interdisciplinary Researchers. He said that he’d put me back in touch with Irwin Guttman, whose apparently now back in Buffalo, rather than at UT. Please e-mail me, Irwin! I’m in need of some more gossip.

(e) Jim Smith (University of Warwick). Thank you for sending me your best wishes, Jim. According to your departmental history, Jeff Harrison, Robin Reed and I founded the Statistics Department at Warwick in 1972. Robin and I subsequently devised the MORSE undergraduate degree, with its first intake in 1975, and MORSE and MMORSE have flourished ever since. You must be able to boast well over 1500 MORSE alumni. Moreover, MORSE Bachelor and Masters degree programs have now been developed at Birmingham. How about a celebratory dinner during 2012, e.g. at that tasty Indian restaurant in Leamington, where Julian Besag drank us all silly?  (Eight pints each following our pre-seminar sherry. That was the night that the IRA bomb exploded in Coventry)

[ I later drank with Julian in the Essenhaus in Madison, which he thought was the worst bar he’d ever ventured into, and into the night in San Francisco.]

(f) Jim Berger (Duke University). It was great to here from another erstwhile drinking buddy again. As far as I could discern, Jim is planning to read my academic novel Grand Schemes on Qinsatorix. Perhaps he’ll discern more implied titbits over a glass of port.

(g) Brad Carlin (University of Minnesota). Brad said that he was glad that I was well enough to have remembered so much. He also said that I’d given the best performance of the Rev. Thomas Bayes that he’d ever seen. When I compared the picture of me returning from Heaven at Valencia 6 with ISBA’s portrait of Bayes, I realised that Bayes and I are virtual look-a-likes!

(h) Peter Lenk (School of Business, University of Michigan). Peter’s Ph.D advisor was my friend Bruce Hill who once said that ‘he was looking forward to hearing why Professor Leonard thought that it was good to be a sure loser’. Peter said that, despite this, my 1978 paper on prior-informative density estimation had greatly inspired his long-time research on Bayesian density estimation. He also sent me a picture of himself as a baby, and a joke, which I couldn’t quite fathom, about a Bayesian dog.

(i) Jan Ondrich (Department of Economics, University of Syracuse) It was great to hear from you again after all this time, Jan. I found your political insights and academic gossip to be invaluable at Wisconsin in1981. Congratulations on your outstanding career e.g. in Bayesian Economics. And thanks for your news about my friend the New York historian Peter Wetzler, whose data are discussed in my 1999 Bayesian book.

(j) Frank Lad (University of Canterbury, Christchurch)  Frank and I attended several of Arnold Zellner’s Bayesian Inference in Econometrics and Statistics seminars, and he was always ingeniously insightful on Bayesian Philosophy. He is now developing the concept of ‘extropy’ as an alternative to entropy. Good luck on that, Frank!

(k) Ben Torsney (University of Glasgow). Thank you for your good wishes, Ben. We first knew each other while we were studying for our Masters at UCL, though your Glesca accent was too strong for me. Please remember me to Jim McNicol (BIOSS).

Jim and I played ping pong together at UCL.

(l) Lars-Erik Oller and Timo Alanko (University of Helsinki , and Head of Statistics Finland)  It was good to hear from you after 31 years, Lars. You and your wife were very kind and hospitable to me in Wisconsin in 1981. I remember the folk singing in your flat in University Houses. I’m glad that you enjoyed my latest homilies about George Box. Congratulations on your medal.

         Thank you for the news about John Duffy, Timo. The best of wishes to John upon his retirement from SHEFC. Please get in contact with me, John, and I’ll take you for a meal in Vittoria. Your latest e-mail keeps bouncing.

(m) Granville Tunnicliffe-Wilson (University of Lancaster) As well as expressing his concerns about the implications of my HEALTH WARNING, Granville requested more information about Florence David. She was Gwylim Jenkins’ Ph.D. supervisor at UCL, and Gwylim was also Granville’s supervisor.

         Florence claimed that she was also George Box’s supervisor at UCL, but George told me that his supervisor was H.O. Hartley. Florence did not always treat her postgraduate students well and she made many of them(e.g. Louis Broekhoven) grind out endless asymptotic expansions. However, many of them were well-trained as applied statisticians with the traditional UCL touch of contempt for mathematical formalisations.

         Dennis Lindley told me that he forced Florence out of UCL in 1967, by telling the Chancellor that he would only accept his appointment to the Chair of Statistics there, if poor Florence stayed in Riverside. There may have been a touch of homophobia, or Dennis’s well-versed hate of weird people, about this. However, Egon subsequently complained to Dennis that Florence was inclined to snoop on the papers in his office.

         Jerry  Klotz told me that Florence was well-regarded and well-loved at Riverside. He also told me about her paramours, whose names I forget. Eric Lehmann was once distinctly demeaning and homophobic about her during a conversation with me and a colleague at Wisconsin, when he compared her with an ‘old chap’.

         Nan Laird interviewed Florence a number of years ago and their conversation was recorded in Statistical Science. Florence came across as an icon of Applied Statistics, and a determined politician who put paid to her opponents on the floor of her Faculty Senate. She is probably a hitherto unrecognized gay icon too. For me, she possesses the stature of Hypatia of Alexandria.

         Tony O’Hagan attended Florence David’s courses, when he was a Stats undergraduate at UCL, at a time when he could obtain a solid grounding in Applied Statistics.        

         I only had the honour of meeting Professor Florence David once, when she was giving a seminar at the University of Warwick. She came across as a redoubtable, though endearing, old woman. I could certainly believe that she smoked a cigar.

Granville’s enquiry jogged my memory about my first ever academic statistical consultancy. When I was a Masters student at UCL in 1970, Dennis Lindley asked me to complete his STATLAB consultancy duties, for the Quairn Professor of English. My client was Professor the Lord Randolph Quirk, and I analysed several contingency tables for him regarding the associations between various linguistic factors. While I was rather pissed off that I had to do this, I spent the evening calculating the different chi-squared statistics. The next day, Professor Quirk was so delighted with the promptness and potential impact of my results that he sent me thirty pounds in a white envelope.

         Baron Quirk later wrote the 1779 page treatise A Comprehensive Grammar of the English Language. He was also Vice-Chancellor of London University.

(n) Ehsan Soofi (School of Business, UW Milwaukee) Ehsan and I took several trips together to Arnold Zellner’s Bayesian Inference seminars, and he once encouraged me to buy a new tie to cheer myself up. He develops Bayesian information measures and applies them to business and economics.

(o) A message from Taskin Atilgan (Taskin was one of my students at Wisconsin. He was awarded his Ph.D. in 1983)

Hi Tom,

         Thank you for your e-mail. I was always curious about the fascinating academicians you had encountered during your illustrious academic life.

         I read it immediately without blinking my eyes. I look forward to reading the full, expanded version.

         I retired in 2003, after spending about 10 years (following Bell Labs) in Wall Street investment banks, a challenging and rewarding place for applied statisticians.

         Now I live in a small remote village in south-western Turkey, on the Aegean coast. I spend my time hiking, and reading books on history and politics. Sometimes I write articles in local papers, and once in a while I get articles published in national papers.

                                     All the best                 Taskin

It’s wonderful to hear from you, Taskin. Maybe illustrious is in the eye of the beholder. Indeed, you may well be one of the most successful of our graduates from Wisconsin. The problem with writing a full, expanded version of my life story is that publishers wouldn’t regard it as credible, even as a novel. In the meantime, perhaps you could consider writing articles about the information in items (10) and (13) of this CDC section.

(p) An e-mail from Graham Wood (McQuarie University). Graham and his family visited Wisconsin during the early 1990’s and I remember enjoying Stephanie’s chocolate cake during a dinner party in my house when we ate well-spiced Cajun food from a local restaurant.

           Amazing to hear from you, Tom, after all these years---have enjoyed reading your life story.

           Coincidentally, I’m currently at Warwick Uni---a quiet research fellowship looking into the genetics of bees and the mite varroa that is causing problems.

                                                With best wishes,


(q) Higgs Boson (20th July 2012).  I have received greetings from Tony O'Hagan (Sheffield) following some advice I sent him about the Statistics of the Higgs Boson. It is of course important to clarify the normality of the sampling distribution of the test statistic, and to consider the p-value and the practical significance, before getting into the ramifications of the prior to posterior analysis. I have recently rejoined ISBA,after founding it with Arnold Zellner in1992, and I look forward to further convivial discussions.

12) The Statistics Group at Edinburgh. I have circulated Bayesian Boy to various powers-that-be in the hope of encouraging the University of Edinburgh to rebuild the Statistics group in the School of Mathematics there. We were seriously mistreated in 2000 when our Faculty Office underestimated and undervalued the immense contributions that we’d made to the University. Please send your messages of support to Colin Aitken.


13) The DNA evidence controversy. During my recent reply to the e-mail enquiries by Professor Norman Fenton of Queen Mary College London, I advised him that:

(A) When I returned to Britain from the U.S. in 1995, I referred to the U.S. version of Bayes Theorem based on the Essen-Moller formula. This assigned a prior probability of 0.5 to the guilt of the defendant and a prior probability of 0.5 to a ‘random man’. Hence equal prior probabilities of 1/2N were effectively assigned to each other member of the population of suspects, where N denotes the size of this population. In situations where there is no preliminary evidence to distinguish between the suspects, it would be much fairer to assign an equal prior probability of 1/N to each and every suspect, including the defendant.

         In the meantime, Peter Donnelly and David Balding had developed more sophisticated versions of Bayes Theorem in Britain. These aspects lead to considerable confusion when I was presenting my arguments to British audiences.

(B) Nevertheless, my key criticisms still hold. These are:

         (a) The combined likelihood ratio R is typically calculated by multiplying together the likelihood ratios that refer to 15 different probes. However 4 to the power 15 is about a billion. This simple calculation is used to justify the ‘one in a billion probability of innocence’ that has been used to convict many suspected murderers, even when the human evidence is in their favour, and many
of them may be genuinely innocent. However the assumption of independence of the DNA probes can only be justified by an assumption of random mating across a homogeneous population. However, our populations are highly heterogeneous and we don’t select our partners at random.

         For example, Phil Dawid has modelled a heterogeneous population by reference to a Dirichlet-Dirichlet distribution, and a spatial covariance kernel would lead to even more convincing results.

         In the extreme situation where the 15 DNA probes replicated the evidence, the combined likelihood ratio in the preceding example would be as low as R=4 rather than as inflationary as a billion.

         (b) For each of the likelihood ratios separately, the distribution of the allele lengths should be estimated using a large enough random sample. However, the data employed are typical sparse and seriously non-random. Therefore the individual likelihood ratios are grossly incorrect, even before they get multiplied. Since point estimates are substituted for unknown parameters, they
can be serious inflated as well as totally biased.

(C) These matters came to a head in the Adams Rape Case and the subsequent appeals. Peter Donnelly, the expert witness for the defence, focussed on extracting prior probabilities from the jury regarding the compelling human evidence, rather on demolishing the much-inflated combined likelihood ratio, in applied statistical terms. Despite Adrian Smith’s protests, the Court of Appeal threw Peter’s application of Bayes theorem out of court. If they had discovered their applied statistical noses in time, then Adams would have been found innocent, as he doubtlessly was.

(D) Professor Fenton invited me to appraise some of the forensic scientists and statisticians involved. I am forced to agree with Terry Speed (personal communication,  Plymouth, 2002) that Ian Evett (British Forensic Science Service) and Bruce Weir (the star prosecution expert witness from North Carolina) insufficient regard for the scientific method and focus too much on maintaining the status quo. In the meantime, Peter Donnelly, David Balding and Adrian Smith are caught up in their intellectuality and fancy mathematics. They should drum up on their data analysis and applied statistics.

         After I published an, all-too-terse, written contribution to a paper on similar topics read by Evett, Smith et al to the RSS, Adrian expressed public outrage to me after a lecture on probability in the Royal Museum in Edinburgh. Unfortunately, he appeared to genuinely believe that he was in the right. 

         I have also recently e-mailed Peter Donnelly and David Balding on these issues.
Why don’t you get this sorted, guys?

(This account is totally based upon my memory, without written record)

See also Bayes Theorum in Criminal Cases, pages 77 - 78, and Bayesian Methods by Leonard and Hsu (1999).


Please click here for The Dean, Jim Crow and the Geneticists for further information


Return to Tom's Home Page


14) The Madison AIDS-HIV data: In about 1985, I analysed the first AIDS/HIV data collected on the campus of the University of Wisconsin-Madison, for the Blue Bus clinic. I, for example, showed that enclaves of students can be mutually protective.

         I then co-organised an interdisciplinary seminar series on AID/HIV issues, with the Nobel laureate chemist Howard Temin
(The Howard Temin Trail was later named after this wonderful man). It was well-attended.


15) Sales of Bayesian Methods (1999, with John Hsu). I have heard from Cambridge University Press’s office in Beijing that our Chinese edition has sold over 2000 copies since 2006. This means that we have sold about 6500 copies worldwide without going to a second edition.

(16) 21st August 2012: The Higgs Boson and the Hadron Collider  (ISBA and Tony O'Hagan)
Tony recently organised a broad-ranging discussion among Bayesians in ISBA regarding the physicists pre-determined standards for concluding that a particle resembles the elusive Higgs Boson.
The physicists require a test statistic to be at least five standard errors from a null hypothesis, under the assumption that the sampling distribution of the test statistic is approximated normal. This corresponds to a p-value of about 0.000005.
I (quite briefly) advised Tony that the main problem is to confirm that the sampling distribution is approximately normal. I somewhat doubt this and, if it wasn't, then the inferential procedure should be entirely different.
Once the distribution of the test statistic has been determined or approximated, then the next problem is for the statistician to use his applied skills, and knowledge of the scientific background to judge whether the difference from the null hypothesis is of practical, as well as statistical, significance. This would probably require some sort of interaction between the statistical experts and the physicists.
Some sort of Bayesian procedure could provide the icing on the cake. However many Bayes factors are entirely misleading and other high flying Bayesian procedures may obscure the applied statistical issues.
This advice is fairly mainstream and most graduates from the Box school at Wisconsin would regard it as quite obvious. In his reply to the numerous statisticians and physicists who joined in the discussion, Tony very much emphasised practical significance.
For his full reply, please click on:
(17) Advice to Abbott Laboratories of Wiesbaden (August 2012): I have provided Natalia Kan-Dobrosky with informal advice concerning my 2002 approach to meta analysis (Statistics in Medicine, with John Duffy). She is computing a Laplacian approximation to the posterior density of the common measure of association for several 2 by 2 contigency tables, together with the corresponding Bayesian significance probability., which effectively generalises a slight modification to Fisher's Exact Test.
Good luck on your applications to clinical trials, Natalia. Don't forget to (a) compare with the posterior densities of the individual measures of association (b) check whether you can really pool the tables, also using our residual analysis, and (c) investigate clinical significance by considering the spread and shape of the posterior densities in relation to the biomedical background.
(18) Sept 13, 2012: E-mail from Orestis Papasouliotos (Merck Group)
Hi Professor Leonard,

I hope everything is fine for you in Edinburgh.

I updated my CV lately, after a few years..., and looking around, found two more references that you can include in your website.

Main, I.G., Li, L., Heffer, K., Papasouliotis, O., Leonard, T., Koutsabeloulis, N., and Zhang, X. (2007). The statistical reservoir model: Calibrating faults and fractures, and predicting reservoir response to water flood. In Jolley, S., Barr, D., Walsh, J.J., and Knipe, R.J. (eds.), Structurally Complex Reservoirs, Geol. Soc. London special publications, 292, 469-482.

· Main, I.G., Li, L., Papasouliotis, O., and Leonard, T. (2007). Improvements in and relating to hydrocarbon recovery from a hydrocarbon reservoir. International patent.

Best wishes,


19) Nov 9, 2012: The real winner in the US elections: Thomas Bayes
As we all know, last night was the US presidential election. In one sense, President Obama was the winner. But in another sense, the real winner was Bayesian analysis, which scored a public relations coup.

In 2008, Nate Silver developed a Bayesian model to forecast the U.S. general election results. He won fame for correctly predicting 49 of 50 states, as well as every Senate race. This brought him a New York Times column and a much higher profile.

This time around, his consistent predictions that Obama was in front earned him a considerable backlash among pundits. While a few criticisms had merit, most were mathematically illiterate, indignantly mocking the idea that the race was anything other than a tossup. Now the results are in, and he has predicted all 50 states correctly.

People with our quantitative background can easily find flaws with this metric. For example, a majority of states were easy to call -- nobody is surprised by the results in Texas or California. More seriously, his "call" for Florida was a 50.3% probability, essentially the proverbial "coin toss". Serious analysis has to chalk Florida up to luck.

Nevertheless, the broader point is that Nate's high-profile Bayesian model just experienced a very visible success. Even better, he recently authored a book-length popular exposition of the Bayesian approach. I purchased that book, "The Signal and the Noise," on a recent flight. It's excellent reading: more technical than McGrayne's recent entry, but no less accessible or engaging.

How can ISBA leverage Silver's success to bring Bayes to a wider audience?

Charles Hogg

20) Dec 20, 2012: Tom is honoured by ISBA

Dear Tom,

I would like to inform you that the ISBA Board of Directors has approved new bylaws on awards, introducing the ISBA Fellows and the Zellner Medal. Celebrating the 20th anniversary of ISBA and recognising those, like you, who contributed to found ISBA, I am very honoured to inform you that the Board has decided to elect you as ISBA Fellow.

Best regards

Fabrizio Ruggeri
ISBA President 2012

P.S. According to the new bylaws, not yet on the ISBA web page,

"D.2.c The purpose of electing ISBA Fellows is to recognize ISBA members who have made outstanding contributions in some aspect of statistical work (publication, teaching, service, etc.)."

14th May 2013:  Greetings from Tom's erstwhile 709/710 student, Professor Neil Gandal, University of Tel Aviv
Hi Tom,

David Steinberg sent me the URL for your writings, in particular, CHAPTER 6: THE UNIVERSITY OF WISCONSIN-MADISON, in which you wrote some nice things about me. I also enjoyed the time we spent together in Madison!

After Madison, my 'odyssey' took me to Israel, California, Boston, and back to Israel in 1991. I have been a Professor at Tel Aviv University since then.

David is also at Tel Aviv Univ - and we ride bikes together once a week. Last weekend, we rode in a 55 km ride for charity (disabled athletes.)

I hope that all is well with you. I'll look forward to reading your story.


  © Thomas Hoskyns Leonard, 2012 - 2013