Tom Leonard - The Life of a Bayesian Boy
6: THE UNIVERSITY OF
Painting of The Mayflower Rose by Fabio Cunha
In what wondrous dream
Do I suppose
I met the Mayflower Rose?
Her petals turned to pink
In a hug and a blink;
Her stem twisted in the breeze
When I fell to my knees;
Her aura turned heavenly and angelic
As I plied her with Dumnonian magic.
But when the prickly thistle flew in,
Rose was gone in the din.
I twisted and turned,
As I drank like a tank for ever and a day.
When Yank fought Assyrian in the Gulf of
She, the Voice behind the Screen,
Spoke as if I’d never been.
Now she beams across the mind waves
In my wondrous dreams.
© Thomas Hoskyns Leonard, January 2013
|Kam Wah Tsui
Department Faculty Skit
participants are Richard Johnson, Grace Wahba, George Box, Tom
Leonard, Tim Reed, and John Gurland.
A Statistics Department student
skit in about Christmas 1990
Tom is played by Joanne
Wendelberger, waking up during a seminar and uttering some totally
pearls of wisdom about the Bayesian approach.
Facebook friend Bob Wardrop with his three grandchildren, Lodi,
hurriedly left a family holiday in Tenby in August 1979 when my U.S.
visa came through, and received a warm welcome from George and Joan
Box in Madison, where I befriended Rich Johnson, Jerry Klotz, Grace
Wahba, George Tiao, Sue Leurgans and the Statistics Department
Associate Chairman Bob Wardrop.
Joan Box was Sir Ronald Fisher’s daughter, and the
authoress of R.A. Fisher, the Life of a Scientist.
George’s two youngest children were Sir Ronald Fisher’s
grandchildren, and I got on well with Harry.
George told me numerous amusing tales e.g. about what
happened when John Tukey visited Fisher for tea, and how Florence
David had once declared, “Don’t get into my car, George Box!” after
George had criticized one of her more boring presentations to the
Royal Statistical Society.
During my first semester, I taught Statistics 775, a graduate course
on Bayesian decision theory, and Wing Wong was my most brilliant
student. In the 50th Anniversary history of the department, Norman
Draper, Steve Stigler et al were to much later highlight my teaching
and research in Bayesian statistics in generous terms (I also
taught 853 Bayesian Inference), together with further contributions
to the Bayesian cause by Kam Wah Tsui and Michael Newton.
During the years that I taught Statistics 775, I was to
have the privilege of awarding A grades to a number of subsequently
distinguished statisticians, including Sharon Lohr, Dennis Lin,
Finbarr O’Sullivan and KyungMann Kim. When I was Chairman of Awards,
I appointed Dennis, whose financial support wasn’t guaranteed, to
his first TA-ship, after he’d marched bravely into my office. He
probably never knew what thin ice he was treading on.
I was to be an active member of more Ph.D. committees than
I can remember. I, for example, made substantive contributions to a
number of Grace Wahba’s students’ theses, and several others.
Ondrich (Economics) and family
From the Archives of the
Mathematisches Forchungsinstitut Oberwolfach
Elizabeth Rose Sanders is the fourth
mathematician from the left
part of my duties at the Math Research Center, I taught several
short courses on Statistics and Experimental Design at military
bases around the US, including the space station in Huntsville,
Alabama, with the late Toby Mitchell who was visiting from the Oak
Ridge National Laboratory in Tennessee and ran for miles every day
to keep himself fit.
Toby was very supportive and introduced me to the key statistical
concept ‘the greater the amount of information the less you actually
know’ when justifying randomization at the design stage, a concept
totally alien to diehard Bayesians.
colleague Toby J. Mitchell (d 1993). Tom and Toby taught Statistics
courses at US Military Bases and the
space station in Huntsville Alabama, together, and visited Washington D.C.
from Adelphi, Maryland in 1980.
everything was going perfectly (I remember going swimming in Lake
Mendota in late October). I was successful at tournament chess (for
example beating the mathematician H.J. Keisler in 19 moves in a chess
miniature subsequently published in a book about the Caro-Kann
defence) and began to recover from my previous academic misfortunes.
catastrophe struck just before Christmas 1979. Following the
machinations of a ruthlessly ambitious untenured assistant
professor, and a weird reference request, I was attacked in the most
vitriolic terms by the British Bayesian establishment, and my
prospects of tenure at Wisconsin were placed in the most serious
George Box and George Tiao gave me considerable support
during the traumas that followed and, rather than being sent
packing, I was, to my surprise, offered tenure early in 1980.
However, in the meantime I lost much of my self-credibility.
During my rebuilding process, I was able to create excellent ties
with Arnold Zellner, a distinguished professor in the Graduate
School of Business at the University of Chicago. Over the years, I
was to attend and contribute a number of presentations to his
twice-yearly series of Bayesian Inference in Econometrics and
Statistics seminars. When I helped organize one in Madison in 1984,
Jim Berger and his cronies stayed drinking into the wee small hours
after a party in my house.
Then, in 1993, I helped Arnold to devise and found ISBA,
the since highly successful International Society for Bayesian
Analysis, and I give myself credit for choosing its name. He was the
first president, and I was the first newsletter editor and a member
of the Constitutional Board. There is a picture of us on the
Internet, taken in the Hotel Nikko in San Francisco, that impressed
my older daughter.
Arnold is perhaps the person who has supported me most of
all in academia. He once described me as ‘light on luggage but heavy
on ideas’. He encouraged my efforts during the early 1980’s to
investigate alternatives to expected utility theory (see Ch. 4. of
Bayesian Methods by Leonard and Hsu, which was not published
until 1999) that could in principle be used by the banks to extract
more profits from their customers when selling portfolios.
From 1980, I also benefited from my friendship with Jan Ondrich, a
chess-playing graduate Economics student from Toronto. I helped him
with some of the Bayesian aspects of his research and he moved on to
become a professor at Syracuse. Not to forget Elizabeth Rose Sanders
from Penn State, who was to earn her doctorate with Norman Draper
before joining the C.I.A. in Washington. Jan and Betsy taught me
more things about academic politics and international academia than
I had ever comprehended. I nevertheless persisted until my
retirement with the foolish notion that ‘life is too short to be
politically expedient’. I also enjoyed my friendship with Neil
Gandal, the captain of the Statistics Department soccer team, for
which I also played near Shorewood Hills, a charming fellow who
would later become a professor in Tel Aviv after obtaining a Ph.D.
in Economics in California.
During 1980, George Box and I planned his exorbitantly expensive and
much-vaunted special year at the Math Research Center on ‘Scientific
Inference, Data Analysis, and Robustness,’ with the help of C.F.Wu.
The idea was to invite a number of statisticians to visit the center
during the year, and to ask everybody to come back and attend a
conference in December 1981.
The conference proceedings were later published by Academic
Press in a volume edited by Box, Leonard, and Wu. The overall
conclusions quite predictably supported George’s and my thesis (e.g.
at Valencia 1) that the Bayesian paradigm is good for inference but
not for modelling.
everything was going well for me once again. But, at the beginning
of 1981, disaster struck one more time. George had emptied his (or
rather the military’s) coffers to invite Dennis Lindley to Madison
as one of the key participants in the special year, because he
wished to debate the fundamental philosophical issues of Statistics
with him. George said that he also wished to offer Dennis the hand
of friendship after a feud that had persisted ever since George’s
international divorce while at Princeton during the late1950’s (that
Dennis regarded as illegal!), since it was better for us all to be
one big happy family.
However, shortly before his arrival in Madison in January
1981, Dennis wrote to George accusing me of having read ‘his letter
of reference’ during my tenure process.
This was pure paranoia, because even I wasn’t quite dumb enough to
have asked Dennis for a reference and I’d never even known that he’d
written a letter about me to Wisconsin, let alone a letter that
hadn’t been officially solicited. Adrian had warned me off several
years previously when I wasn’t appointed to a Fellowship at Oxford
after Dennis had keenly agreed to be a referee and then advised me
that I was well-favoured for the position. That had already made me
wonder about Dennis.
George gave me enough information to conclude that Dennis
was responsible for most of the vitriol in late 1979, that had
almost denied me tenure and sent me back to Warwick. This, quite
surprisingly, came as a big surprise.
Things did not go well between me and Dennis after his arrival,
particularly when he admitted to having attacked my career for the
previous eight years, and moreover brought my erstwhile departmental
chairman Jeff Harrison back into the equation, (after playing silly
buggars over Marie Johnson’s reluctance to give him a parking permit
and refusing to turn up at MRC).
I responded to Dennis much too wimpily and promptly
experienced a frightening mental breakdown during a fit of anger in
my flat on University Avenue, and ended up in Emergency at UW
Hospitals and Clinics.
Until that time, my ‘fogginess’ was caused by my obstructive sleep
apnoea (nowadays I sleep with an APAP machine since I would
otherwise choke every fifty seconds), but I now exhibited more
serious symptoms. My health was not to improve for several years and
I did not properly recover my cognition until some time after my
divorce in 1984. In hindsight, the break-up of my marriage and the
severe downturn in my career seem to have been largely caused by
infighting between other statisticians. Perhaps I and my lovely
family were pawns in a chess game between the gods.
During his semester-long 1981 visit, Dennis described George to me
as ‘pure evil’ since he thought George was ignoring him!! Other
people thought that Dennis was playing the role of punch bag. Dennis
did offer to recommend me for the chair at Manchester, but I
Around that time, Chen Wen Chen, a brave Han Chinese assistant
professor at Carnegie-Mellon was axed to death by the Taiwanese
secret police and left on the campus of the University of Tapei
[this was confirmed by Morry De Groot when he visited Tapei with an
ASA delegation, but the Associated Press reporter Tina Chou was
blackballed by the Taiwanese authorities for long afterwards. Wen’s
death has since been established as a seminal event in the history
This scenario added to my discomfort and made me feel quite
insecure, since I believed, correctly or otherwise, that Wen’s
misfortunes were slightly related to my own (i.e. that there was a
common factor in American academia). I was to receive an unexpected
email during the 1990s that confirmed my suspicions. The intrigues
were certainly well understood by a selection committee for the
Chancellorship of the University of Taiwan. I first learnt, in 1981, about the
academic intrigues surrounding Wen's murder when one of my teaching
assistants at Wisconsin was cruelly and quite unfairly bad-mouthed
to a senior faculty member. One of my first sources of information
was a highly respected Chinese professor of mathematics at Penn
State. The Sino-American academic
intrigues in the United States that may have led to Wen’s death are
alluded to in Chapters 11 and 20 of my novel Grand Schemes on Qinsatorix [where Fleance leads a rebellion of the golden-skinned Icarians following
his brothers’ deaths and his persecution by the ‘Admiral’]. My
sources of information are clarified in detail in the Author's Notes
preceding my novel, though a couple of my senior colleagues at
Wisconsin remain anonymous.
Wen Chen (1950 - 1981)
Han Chinese Martyr
best memories of MRC’s special year are walking across campus with
Hiro Akaike, watching several episodes of Brideshead Revisited
with Mike Titterington and his wife in their apartment in University
Houses, climbing the post-ice-age cliffs at Devil’s Point with Mike,
and with Phil Dawid, and lunchtime conversations with Michael
Goldstein and Peter Green.
Tunnicliffe-Wilson visited with his family sometime afterwards from
the University of Lancaster. We went swimming together and developed
a long-lasting acquaintanceship. I talked at length to him at an RRS
Environmental Statistics Meeting in Edinburgh in 2002, when the
speaker turned up a couple of hours late.
Although I was spaced-out and anti-social for most of the 1981
special year, I managed to develop a conditional Laplacian
approximation to predictive and marginal distributions, via a
backwards application of Bayes Theorem, very essentially after using
a preliminary normalising parametric transformation. (a device
ignored by numerous later authors). This was published in my short
note in JASA (1982) and by Leonard and Novick (Journal of
Educational Statistics, 1986). It predated efforts by
Kass,Tierney and Kadane, who obtained asymptotic saddle-point
accuracy but did not typically apply their approximations in a
manner which would ensure the excellent finite-sample-size numerical
accuracy observed by John Hsu in his Ph.D. thesis, and by Leonard,
Hsu and Tsui (JASA, 1989)
breathed a sigh of relief when Dennis Lindley decided, for reasons
best known to himself, not to return to Madison for the, highly
successful, December 1981 conference on Scientific Inference,
Data Analysis and Robustness, as agreed. George Box promptly
declared victory since he felt that Dennis had ducked out of a
possibly embarrassing intellectual debate.
I recall being soundly told off at the conference by George
Barnard for my positive interpretation of Birnbaum’s 1962
justification of the Likelihood Principle, a viewpoint so
convincingly taught to me by Phil Dawid and which Jim Berger has
advocated in his monographs ever since.
Bob Hogg was much more supportive e.g. about my proposed
inductive procedures for model selection, and that was to lead to
even further intrigue the following year when he used them to tease
Dennis’s erstwhile ‘sugar daddy’ Mel Novick in Iowa City.
glad that I left the U.S. Army’s Math Research Center in 1983; the
director had been trying to coerce me into working (along
with C.F.Wu, who was much more dedicated to the cause and developed some
outstanding theoretical results), on a thinly-disguised experimental
design problem that turned out to relate to the optimal way to aim
nuclear missiles at silos.
my shame I did publish a couple of MRC technical reports on the
topic (including An Inferential Approach to Quantal Response, MRC
Technical Report, 1982) and I asked my project assistant Michael
Hamada to do a few simulations. The idea was to base the choice of
the design measure on the posterior density of the effective dose.
In 1996, I published these ideas with John Hsu, totally disguised
and with due acknowledgement, in a paper on biossay in Modeling
and Prediction : Honoring Seymour Geisser. But my ideas were, as
far as I know, never implemented by the military.
Michael Hamada is now a highly-accomplished statistician at
the Los Alamos National Laboratory in New Mexico. He has published a
prestigious book on the Design of Experiments with C.F.Wu.]
have all sorts of other fascinating stories to tell e.g. during one
consultancy we were advised that the military would fire three
Pershing missiles each time they tested them since they needed to
keep three departments happy.
A statistical conference that George and I attended in the
Naval Postgraduate School in Monterey, California was hijacked by
several generals, one of whom declared that ‘a small amount of
brutishness is worth lots of pity’. Bradley Efron expressed his
dismay when he got to present his paper about the bootstrap. To his
enormous credit, George, who benefited from hefty grants from the
military for purely academic research, had once told them to go
forth and multiply, or words to that effect, when they tried to take
him up in a helicopter to review the troops. When the generals
persisted in controlling the Monterey conference, he took us for a
walk along the beach.
[The totally fictional character Professor Brad Redfoot in my novel
Grand Schemes on Qinsatorix is very slightly motivated
by George. The campus of the University of the Sunrise in Trivoli is
modelled on the campus of the University of Wisconsin-Madison]
MRC’s total disregard for Wisconsin State Law (by not focusing on
purely academic research) was to lead to its final demise during
the Gulf War in 1991 after the students on campus got wind of the
less salubrious activities and protested to Chancellor Donna
Shalala. I’m still trying to track down an article I published in
The Daily Cardinal. I do recall Rich Johnson’s reaction
to reading a stray copy of the article, and a graduate student from
another department using my revelations as the basis for his
detailed report on the controversy.
Rich told Jerry Klotz and me later, during one of his
informative lunch-time conversations, that John Nohel, the long-time
Director of MRC, had been dragged out of bed to explain himself on
these issues. As my colleague Bob Miller so aptly remarked ‘it
couldn’t have happened to a nicer person’. Now Bob was a gentleman!
Before I left MRC in 1983, I used the expertise there (Ben Noble,
Dennis Cox, and an intensely theoretical Jewish visitor whose name I
cannot recall) to formulate a new Bayesian approach to the
estimation of a covariance matrix, using a matrix logarithmic
transformation and a multivariate normal prior. The prior to
posterior analysis was virtually impossible and I needed to refer to
a Volterra integral equation. (Dennis also advised me regarding the
Statistics of Paternity Testing, and this was to get me into
numerous Mid-West court cases.)
Because of my health problems, I wasn’t able to take any credit for
this until much later, and a number of other potentially successful
projects went by the wayside.
Brian Yandell and Tim Read, both assistant professors, were two of
my drinking companions around that time, and I remember both of them
on one occasion becoming quite convivial. Brian was more recently
appointed Chairman of Statistics, but handsome Tim (who’d published
with Noel Cressie and worked in Biostatistics with David De Mets)
disappeared and I haven’t been able to trace him since. Maybe I
yearn for too many lost friendships. Where is everybody now?
17th July 2013: An e-mail from
Great to hear from you after so
long and to hear you are doing well! I enjoyed seeing
the pictures and reading your web-page which brought
back a flood of memories from those years! I have
attached a more recent picture so you can see the
effect of time.
After leaving Wisconsin in '84, I
went to work for Hewlett-Packard in the Bay Area at
their Stanford Park Division. After 4 years, it was
time for a change and I went on a one-year backpacking
trip with my wife across Africa and much of Asia which
was a life-changing experience. On our return to the
US at the end of '89, I went to work with DuPont in
Wilmington, Delaware where I remain to this day ...
something I never expected, however the work has been
interesting and diverse, including 6 years developing
teams back in Asia (Singapore and Shanghai).
Currently I am working with our new Biotechnology R&D
organization based in California, lots of interesting
challenges and lots of cross-country red-eye flights
for the time being...
Wishing you all the best for the future and thanks for
getting in touch!
Read (thirty years later!)
David De Mets was perhaps the most actively political academic I’ve
ever met, and that’s saying something. He reportedly kept private
files on every member of the Statistics department in his office.
But he was able to build a prestigious Biostatistics empire in the
Medical School, albeit at a human price, with outstanding creative
research and medical consultative contributions from the likes of
Rick Chappell. Michael Newton and Kyung Mann Kim. David’s own
research was a bit on the dry side.
[The Fundamentals of Clinical Trials? Isn’t that pie in the sky?
It’s impossible to sufficiently replicate statistical experiments in
medicine, and large enough sample sample sizes for practical
significance and effective randomization are usually well nigh
impossible in situations where objective conclusions are sought
Around this time, Taskin Atilgan from Izmir developed an empirical
model selection criterion EIC with me, which referred to the ridge
that appears on graphical plots of the log-likelihoods of nested
models. While EIC wasn’t quick-and-easy, it compared well in
empirical studies with both AIC and BIC.
Taskin worked and published, on the side, on tRNA sequences in
bacteriology. He also published several joint papers out of his
thesis, including one with me (in 1987) on penalized likelihood
procedures for smooth bivariate density estimation, after moving on
to Bell Labs. During his Ph.D. celebrations in 1983 almost the
entire Turkish community of Madison partied in my house.
During 1982, Bob Hogg, who’d listened in awe to my presentation at
the December 1981 MRC conference in Madison, invited me to visit the
University of Iowa to give a seminar on my views about Bayesian
coherence. He was a most hospital host, before vanishing before
dinner to watch a basketball game. Unfortunately, my old friend Mel
Novick was suffering from an unexpected heart attack at the time,
and wasn’t able to attend my seminar as he’d planned. The next
morning, Bob quickly sent me packing back to Madison, and I was
rather slow on the uptake in realising why. My step mother was later
most appalled to hear this academic story, and I feel bad about it
visited Iowa City for a fourth time during the Summer of 1984, and
spent three months at the Lindquist Center for Measurement with Mel,
with whom I’d worked at the American College Testing Program in 1971
and 1972 when I was a student, and he’d taken me out for enormous
meals. While he’d never encouraged me to publish my research with
him, he implemented some of the suggestions in my five A.C.T.
technical reports in a 1975 paper in Psychometrika that
earned Charlie Lewis his tenure. Maybe that was fair. Mel paid me a
total of $1200 for my efforts, and they did reference one of my
technical reports, but Ming-Mei Wang put the paper together.
Maybe Mel and Charlie chose the numerical example.
[Mel had made himself famous at the Educational Testing Service in
Princeton in 1967 by publishing the seminal text Statistical
Theories of Mental Test Scores with Frank Lord, but with
magnificent contributions by Allan Birnbaum who was shamefully
dropped by Lord as a co-author and didn’t bother to check the
proofs. While Mel was Dennis Lindley’s erstwhile long-term ‘sugar
daddy’, he’d fallen out with him in 1981 over something or other.
Irwin Guttman once explained Mel’s more general psychology to me by
describing him as ‘the fat boy on the block’]
However, I was delighted, in1984, to receive three months salary out
of Mel’s enormous ONR grant, since I would have otherwise been skint.
During my stay, in an office behind the celebrated ‘Bayes
barrier’, I was to complete some interesting research with Mel on
Bayesian Full Rank Marginalization for Two-Way Contingency Tables,
which he insisted on publishing in The Journal of Educational
Statistics (1986), even though the referee thought that it was
of high enough quality for JASA.
JES paper includes our analysis of the Marine Corps Data,
where we were able to combine our new theory with statistical
modelling in relation to the data and scientific background, in
order to partition and collapse the table. This analysis was
favourably discussed following a seminal paper on the chi-squared
statistic in the Annals of Statistics (1985) by Efron and
Morris. Brad and Carl compared my approach with their own.
also helped Mel and a his hard-working Ph.D. student Shin Ichi
Makeyewa to develop an Empirical Bayes approach to factor analysis,
using shrinkage estimators for the variances, and this seemed to
work well in practice since it avoided the anomalies (e.g. factor
loadings close to zero) of maximum likelihood. I guess that it’s
been published somewhere too, and I’m still hoping that I was a
Mei-Ming Wang was a chatterbox. She told me that when Mel
was editor of The Journal of Educational Statistics,
the material in some of the rejected papers got published by other
authors, but I have no way of ascertaining whether she was correct.
During my 1971, 1972 and 1984 visits to Iowa City, I sketched out
several new hierarchical Bayesian approaches to Item Response
Theory. [e.g. ONR Technical Report 85-5, 1985, has, according to my
records, been cited in the psychometrics literature, by Robert J.
Mislevy of E.T.S. and others, as a major treatise on Birnbaum’s
two-parameter logistic model]
1994, I was to co-author a paper in Psychometrika on this
topic with Frank Baker and Seock-Ho Kim of the University of
Wisconsin, after helping Kim to complete his Ph.D. thesis in
Educational Psychology. In 1991, I’d published another paper in
Psychometrika, with John Hsu and Kam Wah Tsui and concerning
extra-binomial variation alternatives to the beta-binomial model.
Maybe I’m a psychometrician by trade. I’m currently working on more
math for the two-parameter normal ogive model, in an attempt to
pragmatise Jim Albert’s prior-informative MCMC approach. Kim has
recently written a book with Frank Baker, also on Item Response
Theory, and he is now a prize-winning Professor of Educational
Psychology at the University of Georgia.
During the Summer of 1984, Mel and I visited the Educational Testing
Service’s Frank Lloyd Wright building in Princeton. We were met by a
hostile Frank Lord and I learnt how the Office of Naval Research
doled out its enormous grants to the psychometrics profession. This
was not purely on merit.
When I returned to Madison in the Fall of 1984, I became depressed
again and my career seemed to relapse into its previous unproductive
turmoil. However, my colleague Kam Wah Tsui helped me in two
different ways during 1985.
Firstly, Kam encouraged me in my renewed spiritual beliefs. While
Blackhawk Evangelical Free Church wasn’t exactly perfect for a free
thinker like myself, the activities there helped me to build up my
self-esteem during the next seven years, and I taught Sunday School
for some time. But the wolf seemed to throw off its sheeps’ clothing
during Bill Clinton’s presidential election year. The
broadly-defined ‘Campus group’ met for bible readings in my house on
Pickford Street and all sorts of real-life experiences, including
shootings in Texas, were discussed. Blackhawk expanded rapidly
during the conservative backlash in Madison, and now has several
thousand zealous members. Maybe Chief Blackhawk of the Sauk is
turning in his grave.
also persuaded me to suggest a research problem for his beginning
Ph.D. student John S.J. Hsu, and we proceeded to effectively jointly
supervise him. It was John who first demonstrated the excellent
numerical accuracy of sensibly-formulated conditional Laplacian
approximations (Leonard, JASA 1982), an accuracy that
continued right down the tails of the approximate marginal posterior
densities. A generalisation to approximations to the posterior
densities of non-linear functions of the parameters provided enough
material for the first half of John’s 1990 thesis (see Leonard, Hsu,
and Tsui. Bayesian Marginal Inference, JASA 1989).
For the second half of his thesis, John developed a
Bayesian analysis for mixtures, and this was later published in
Ann. Inst. Stat. Math. with an interesting application to the
estimation of survivor distributions for the Madison colon cancer
data where some of the observations are censored. Fluoricil-6 was
apparently the most efficient drug, but only because a number a
patients dropped out of the trial because of the drug’s severe side
I published a number of papers with John after he’d moved
on to the University of California at Santa Barbara, and our 1999
book. These included a joint paper in Statistica Sinica with
Doug Bates’s student Christian Ritter.
[Doug, who was one of George Box’s closest buddy’s, was one of the
most prolific members of the department e.g. his research on the
geometry of non-linear regression and his development of our
department’s computer system; he’d worked with Don Watts at Queen’s
University. Don was a former STATLAB director in Madison, and his
musical wife Valerie once played for the BBC. I once partied with
them at their beautiful farm in Ontario, though the top soil was
extremely thin. Christian followed in Doug’s footsteps by using our
Laplacian t-approximation to analyse a tricky non-linear regression
model in chemistry. Christian is now happily married to his
fellow-student Linda Danielson and working with her at the Catholic
University of Louvain.]
best paper with John Hsu was undoubtedly Bayesian Inference for a
Covariance Matrix, that appeared in the Annals of Statistics
(1992). John helped me to finally unravel the complicated math that
I’d formulated at MRC in the early 1980’s, by reference to the
recursive solution of Volterra equations developed by the
mathematical physicist Richard Bellman and numerous tricks with
eigenvalues and eigenvectors.
Our multivariate normal prior for a diagonalization of the
matrix logarithm of the covariance matrix provided a very general
alternative to the inverted Wishart conjugate analysis developed by
Gwyn Evans in 1965, and John’s computations of the exact marginal
posterior densities of the parameters of interest were ingeniously
devised. They yielded a generalisation of my Technometrics
(1975) method for the simultaneous estimation of several
log-variances, which came out of my 1973 Ph.D. thesis.
Other authors (e.g. the economist Neil Shepherd) have tried
using a multivariate normal prior for the logs of the variance
components of a general covariance matrix, but it is then virtually
impossible to maintain positive definiteness of the matrix. None of
the economists seem to have even heard of my Technometrics
paper, since they never cite it, but I don’t get worked up about
these things any more. They’ve probably never even heard of
An Associate Editor, who I assumed to be Jim Berger, was
instrumental in encouraging us to rewrite the first submission in
more rigorous terms, and I sometimes wonder (I’ve forgotten why,
though I remember some comment about bees) whether the kinder of the
referees was Dennis Lindley. The published version, which appeared
at the front of the journal (this impressed Arnold Zellner, if
nobody else!), was to earn me a $5000 salary rise, and I have Doug
Bates to thank for that.
During my years at Wisconsin, I taught 709-710, a very advanced
mathematical statistics course that prepared students for the
totally sadistic Ph.D. qualifier, but we all needed to be primed on
the Berkeley-style asymptotics by my teaching assistant Doug Nychka.
Doug, who is now the Director of Mathematics in the Geosciences at
NCAR in Colorado, was one of the several of Grace Wahba’s
‘Splinemen’ who possessed a keen eye for practical data.
A Splineman called Jim Wendelberger was also born to live
in America. He produced the thickest Ph.D. theses (on world climate
maps) that I’ve ever had to examine. He married Joanne Roth and I
danced with Grace Wahba at their wedding. Joanne later impersonated
me during one of the more poignant Christmas skits in George Box’s
house, waking up as a talkative arch-Bayesian after nodding off with
my shirt hanging out during a seminar about something entirely
Jim and Joanne moved on to highly successful careers and
their three daughters are also successful statisticians. I regularly
played pool with Jim in the Badger Tavern and one of our opponents
once broke his pool stick over his knee after scratching on the
Jim is currently Director of Statistical Analysis for
Urban Science in New Mexico, and Joanne is a group leader at the
Los Alamos National Laboratory.
Grace’s Splinemen were, with one or two exceptions, usually very
kind to my work. However, a hard-pressed Director of STATLAB, who
was really quite a decent fellow, once borrowed my 1982 MRC
technical report describing a novel Empirical Bayesian approach for
semi-parametric logistic regression models from my office, converted
it into splines, tagged on a heart disease data analysis, and
published a modest generalisation in a subsequently well-cited paper
in JASA! Such is the fate of the creative. Everybody else
needs their meal ticket too.
also taught many sections of the interdisciplinary courses
Statistics 201 and 301, and the mathematical statistics sequence
311-312 for undergraduate Industrial Engineers. I got into a
fascinating political saga after I described the ‘Rachel Welch’
density (the perfectly-smooth bimodal density of the reciprocal of a
standard normal variate) to the I.E. students. One of their more
redneck senior professors, called Big Steve, I think, didn’t approve
of me taking them to the Badger Tavern for a drink and tried to get
at my teaching evaluations, the miserable bastard. Perhaps he was
scared of me introducing them to Rachel Welch.
Several of my Statistics 775 students, including Jean Deichtmann and
Josep Ginebra-Molins, helped me to modify my alternatives to
expected utility theory, which are discussed in Chapter 4 of my book
Bayesian Methods. Josep is now a professor at the University
Polytechnique of Catalonia in Barcelona.
The advanced undergraduate course Statistics 431 was
extremely enjoyable to teach. I highlighted my version of ‘Goodman’s
full rank interaction analysis’, quasi-independence models, and the
problems with lurking variables that surround Simpson’s paradox. I
encouraged the interdisciplinary students to apply this methodology
to data sets from their own areas of interest, and to seek real-life
conclusions e.g. by interpreting the patterns of the residual
interactions in relation to the background of the data.
The 431 students’ individual projects seemed to create a huge
amount of social impact in a wide variety of areas (I for example
recall an impressivc analysis of the dancing routines of Wisconsin
cranes, and a subjective analysis by a nice young lady of drug abuse
rates on the Madison campus that refuted the official figures of
about 10% by a ratio of three to one), and the students took my dire
warnings about lurking variables to heart, on occasions quite
Alistair Scott, who was visiting from Auckland, and Jerry
Klotz were amused when one of the students advised the press that
‘Professor Leonard says that you should consider all the lurking
variables before drawing any conclusions’. Alistair thought that I
had lurking variables on the brain, and Jerry asked me what they
George Box always thought that Jerry had a beautiful wife.
I enjoyed going canoeing with him, and we once almost got stuck
without a paddle together of the Yahara River. He was highly
regarded in non-parametrics, and the discoverer of the Klotz test
for heterogeneity of variances.
I have since published the 431 course material in A
Course in Categorical Data Analysis (Chapman and Hall, 1999,
with contributions by Orestis Papasouliotis), but the
simply-expressed book was, to my disappointment, said to be too
difficult for the students by some of the expert reviewers, and
While I was teaching 431, I helped a Geology graduate student called
Dennis Kerr to develop new methodology for analyzing geological
layers using suitably normalised quasi-independent contingency
tables to estimate the transition matrices in Markov chains.
also developed a neat modified profile likelihood procedure, based
upon broken and unbroken plate models, to estimate the bottom of the
Mid-Continent Rift, for Jon Nyquist, a geology Ph.D. student, fellow
chess player, and Antarctic explorer. The methodology is published
in 'Flexural Modelling in the Mid Continent Rift', by Nyquist and
Wang, in the Journal of Geophysical Research (1988). Jon is
currently a Professor of Geophysics at Temple University.
1987, I presented the ideas in Statistics 431 in a American
Statistical Association short course on Applied Categorical Data
Analysis in the Hilton Hotel in San Francisco, and they were
1986, I was the statistical expert for nine nursing homes in their
case against the State of Wisconsin that attempted to force the
State to re-imburse their actual costs. Our first success was to
take an appropriate random sample, that could be split in two, from
the Wisconsin population of nursing homes. We then used SPSS to give
us a bivariate scatterplot of the reimbursed costs and the actual
costs for the nursing homes in the sample. When we observed a
strange bloop in the plot, we realised that a regression analysis
was both unnecessary and inappropriate. Our scatterplot amply
demonstrated that it was only the expensive nursing homes which
weren’t adequately reimbursed. When I suggested using a Kolmogorov-Smirnov
test, the lawyer replied, “That’s a good idea. Let’s go for a
was later the statistical expert witness for the defence in a case
where the State of Wisconsin alleged that Poly America Inc. were
selling underweight polyethylene sheeting. I completed an extensive
data analysis, but I don’t remember the outcome.
In another case, Rite Hite Corporation claimed substantial
damages against Kelley Co. Inc for loss of profits after a patent
infringement. I managed to tip the case in favour of the defence by
sending their lawyer into court with a copy of Box, Hunter, and
Hunter, where he used the Oldenburg Stork Example to convince the
judge that the plaintiff’s correlations were entirely spurious.
During a bizarre defamation case against Wisconsin Farm Bureau, a
court official appeared at my office door and attempted to subpoena
both me and Mendel’s pea-breeding data.
In 1992, I successfully challenged an alleged 99.99994%
probability of paternity, based upon DNA evidence, in Phillips,
Wisconsin. In the same year, I helped Wisconsin Lotteries to win an
age discrimination suit. I was involved in a number of cases
involving HLA blood typing and DNA evidence, but I always declined
the Chicago murder cases. I was an accredited expert witness in the
States of Wisconsin, Minnesota, Iowa and Illinois.
screwed up in a case where I was supposed to be defending the
Wisconsin Department of Justice against accusations from several
prisoners in solitary confinement that their cells were going red
hot and icy cold. The data collected by the Justice Department were
so ridiculously spurious that I tried to side with the prisoners
pro bono, and the powers-that-be were totally unamused.
Between about 1985 and his tragic death in 1994, I substantially
benefited from my intellectual friendship with my neighbour James A.
Koutsky, a UW professor of chemical engineering and president of the
American Ceramics Society, who liked the work on modelling by
mixtures that we used to analyse the Madison colon cancer data and
wanted to apply it to chemical process data. He thought that ‘the
human race will go to the stars’ and that ‘our wisdom is with
grandmothers’. While heavily agnostic, he also conjectured that gay
and lesbian people were created as extra uncles and aunts at the
beginning of time, for the purpose of giving additional support to
our traditional families.
James A. Koutsky
literary colleague Allan and I have since called this ‘Koutsky’s
hypothesis’, and we only wish that the gay community would take heed
of it. It certainly isn’t open to refutation by the creations
accounts in Genesis, where it is claimed that God made humans in his
own image, male and female alike. However, the head of the Edinburgh
LGBT Centre on Howe Street once gave Allan a very blank look. I
think that numerous self-appointed and unqualified gay activists,
including a publicly-agnostic retired Bishop of Edinburgh who still
expresses his individualistic views from the pulpit at my church,
are too keen to perpetuate the myth that people who regard
themselves as gay are inherently different.
While I was in Madison, I informally counselled many
actively gay people, and I was for a time a local convenor of
Integrity-Dignity, a religious organization that was supportive of
them, but which had been thrown off holy ground by Cardinal Josef
Ratzinger. As I was also the co-organiser of an AIDS/ HIV Ministry
and challenged various leading fundamentalists in group debate, I am
therefore well-qualified to talk on gay social issues. However, my
apparently liberal church in Edinburgh adheres to the PC line and
has never invited me to speak. Indeed, they buried an article by
Allan and myself on gay issues, the traditional family structure and
Koutsky’s hypothesis that we submitted to them for discussion in
2006, and the rector glowered at me for over a year.
Richard L. Brown, M.D
During the early 1990’s, I helped Dr. Richard L. Brown of the UW
Department of Family Medicine to apply for an NIH (National
Institute of Health) grant to develop a questionnaire that might
help to screen potential drug users, who often give false responses
in order to protect themselves from prosecution, by asking them
conjoint questions about drug and alcohol (i.e. substance) abuse.
The gold standard for defining a patient to be a drug abuser was a
potentially inaccurate 853 item questionnaire! Rather than using
factor analysis, as previously recommended to Richard, to reduce the
number of items, I suggested seeking the advice of groups
experts, drug abusers, and recovering drug abusers. The recovering
drug abusers were the most insightful, and they helped us
the number of potential items to about nine. We then asked NIH to
fund a couple of large surveys that might help us to develop a
simple two-item questionnaire with reasonable sensitivity and
specificity, and to confirm that this would be similarly efficient
for patients with different characteristics and ethnicities.
When the grant came through, we appointed Orestis
Papasouliotis, a broadly-qualified Statistics graduate student from
Salonika, to be our research assistant. He helped us to design an
efficient conjoint questionnaire where the patient was screened as a
possible drug abuser if he answered positively to at least one out
of two simple questions, and we published three papers with him and
Laura Rounds in family medicine journals. Rich was awarded tenure on
the basis of our results. He is still using a version of our
Wisconsin Substance Abuse Questionnaire to screen potential abusers,
and thousands of drug-abusing Wisconsinites have benefited from our
Around that time, I collaborated with Kam Wah Tsui on the
supervision of two more of his Ph.D. students, Mohamed T. Madi and
Tom Y.M Chiu. This led to a paper with Madi on Bayesian estimation
for shifted exponential distributions that appeared in the
Journal of Planning and Inference (1996). He’s now a Professor
and Associate Dean at the University of the United Arab Emirates.
[See also item (1) in CDC section.]
And we encouraged Tom Chiu, even though he was dead scared
of the maths, to follow up on my 1992 paper with John Hsu, by
developing a matrix logarithmic model for several covariance
matrices, combined with a linear model for the mean vectors. We used
maximum likelihood estimators for the unknown parameters and
attempted to prove their asymptotic normality. This proved to be a
monumental task, and Tom and I needed to spend our Saturday mornings
struggling through exceptionally complex versions of Berkeley-style
asymptotics, while Kam prompted us during the week.
Our results were published in our 1996 paper in JASA
and I’m proud of the theorems, if not the tentative practical work.
Tom Chiu moved on to become a master statistician with SPSS in
Chicago, and he has since advanced further. I was invited his
traditional Chinese wedding, and this was a wonderful experience.
random effects version of the matrix logarithmic model relates also
to the Leonard-Hsu 1992 Bayesian paper in the Annals of
Statistics. It has been successfully applied by a number of
econometricians, including James Le Sage and Kelley Pace, to
multivariate time series and spatial random effects models, and can
explain multivariate stochastically volatile data. I was delighted
to discover these applications in my retirement during a Google
search. The econometricians have given us lots of credit, which is
Maybe somebody (e.g. another of Kam’s students) would like
to use our Volterra integral equation/spectral decomposition
technique to derive the Jacobian of the matrix logarithmic
transformation. It would be very useful to be able to use the
Jacobian when developing importance sampling procedures for random
covariance matrix models.
Christian Ritter and their son
During early 1995, I summoned up enough courage to visit Britain for
the first time in sixteen years. After a nostalgic stay in London, I
met up with Professor Tony O’Hagan and his wife Anne in Nottingham.
They were most hospitable, and Tony told me about the vacant Chair
of Statistics at Edinburgh.
I decided to apply for David Finney’s former chair in order
to be closer to my daughters in England, and because my nephew and
his family were living in Edinburgh; he’d recently graduated from
the University’s medical school. I consequently found myself
returning to Britain one more time (while I was recovering from some
nasty surgery in Wisconsin) and explaining away my U-shaped career
to a formidable interviewing committee in the Old College of the
University of Edinburgh.
Mike Titterington and Adrian Smith were the external
advisors to the committee, but I was remarkably unphased. To their
credit, they followed the British tradition of reading several of my
publications. These included my 1992 Annals of Statistics paper with
also sent Mike and Adrian a copy of a highly mathematical
single-authored article that Rich Johnson had accepted for
Statistics and Probability Letters (1996), after giving me
substantial help and advice. In this article, I proposed using a
multivariate Dirichlet process as a mixing distribution when
constructing an exchangeable sampling distribution for uncontrolled
data. This related to research that I’d completed at MRC during the
early 1980’s, but which I’d failed to extend and apply well enough
to get published in JRSSB.
During my interview, I tried to sound perceptive and visionary. To
my surprise, Vice-Chancellor Sir Stewart Sutherland subsequently
offered me Scotland’s premier Chair of Statistics, even though there
were at least three highly qualified further applicants, including
two incumbents of other Scottish chairs. When I accepted, I took a
year’s leave of absence from Wisconsin as insurance. I succeeded in
selling my house by Lake Wingra for a handsome profit, just in time
for my move. I always land on my feet, according to Rich Johnson at
Early in August 1995, I visited the Mexican festival in Santa
Barbara with John Hsu, before leaving Madison on the bus for O’Hare
airport. By the end of the month, I was watching the human circus
on the Meadows, at the Edinburgh Festival, and I haven’t set foot in
the United States since. I learnt shortly afterwards from my older
daughter that Edinburgh was one of the highest-ranked universities
in Britain, and even compared with Oxford.
Around the time of my departure from Madison, Gouri Bhattacharyya,
who’d appointed me to my position there in 1979, retired
unexpectedly early. While I heard some whispers across the lunch
table, I can only guess at the political machinations that lead to
this decision. Gouri was a brilliant, and charming, gentleman,
though he would insist on attending the departmental picnics in
Vilas Park in an officious-looking suit.
John and Serene Hsu, Santa Barbara,
California (Christmas 2012)