The Life of a Bayesian Boy
CDC Section: Contributions, Discussion and Corrections
Please submit your
They may be lightly edited.
||My joint work
with Mohammed Madi
contributions to density estimation
||My 1978 ICL
lecture notes on Bayesian categorical data analysis
Robinson’s research on Bayesian template modelling
vacation work (1969 and 1970)
||A key reference
appeal (Epilim Crono and other physically damaging mind control
response to Bayesian Boy
Group at the University of Edinburgh
||The DNA Evidence
||Sales of Bayesian
Methods (1999, with John Hsu)
||The Higgs Boson
and the Hadron Collider (ISBA and Tony O'Hagan)
Advice to Abbott
Laboratories of Wiesbaden
Orestis Papasouliotos (Merck Group)
||The real winner
in the US elections: Thomas Bayes
||Tom is honoured
Tom's erstwhile 709/710 student, Professor Neil Gandal,
University of Tel Aviv
|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?
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
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.
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.
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
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
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
email@example.com 2nd. May 2012
slightly edited, and occasionally paraphrased
Hi Professor Leonard,
Please find some
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.
practical and MCMC Bayesian techniques for my heterogeneous variance
ANOVA model to the analysis of this
n=67 Stanford students
n=22 Scottish rapists
n=40 Scottish paedophiles
n=20 Scottish murderers
n=128 Stanford medical patients
I began with a
comprehensive analysis of the visual functions neuropsychological
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
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
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]
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
estimators to smooth the graduate intakes to the Edinburgh Law
School. [This paragraph is paraphrased—
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
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.
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
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
When I recovered, in October 2011, from my six months of
somnolence, lack of mobility, only a modicum of cognition,
surgeries for cancerous melanoma
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
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
THE RESPONSE TO BAYESIAN BOY
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
‘Bayesians never die, but their data analyses go on before them’
(b) Norman Draper and Murray Clayton (University of
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
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
(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
(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)
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
(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
(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).
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
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
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)
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
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
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.
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.
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:
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
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.
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
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
serious inflated as well as totally biased.
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.
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
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.
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
Please click here for The Dean, Jim Crow and
the Geneticists for further information
Return to Tom's Home Page
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
(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
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
(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
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
|(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.
|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
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
|20) Dec 20, 2012: Tom is
honoured by ISBA
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.
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
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
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
I hope that all is well with you. I'll look forward to reading your