Tom Leonard - The Life of a Bayesian Boy    


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 Tears,

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


George E.P. Box   Grace Wahba   Richard A. Johnson   James Hickman (1927-2006)
Kam Wah Tsui   Brian Yandell   Murray Clayton   Sue Leurgans
A Statistics Department Faculty Skit
Madison, Wisconsin, Christmas, 1983
The participants are Richard Johnson, Grace Wahba, George Box, Tom Leonard, Tim Reed, and John Gurland.
A Statistics Department student skit in about Christmas 1990
Tom is played by Joanne Wendelberger, waking up during a seminar and uttering some totally irrelevant
pearls of wisdom about the Bayesian approach.
Tom's Facebook friend Bob Wardrop with his three grandchildren, Lodi, Wisconsin, 2013


I 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.

Doug Nychka Neil Gandal Finbarr O'Sullivan Jim Wendelberger Joanne Wendelberger
Jan Ondrich (Economics) and family
From the Archives of the Mathematisches Forchungsinstitut Oberwolfach
Elizabeth Rose Sanders is the fourth mathematician from the left

As 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.

Tom's 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.

So 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.

But 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 doubt.

         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.

Jim Berger

         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.

So 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 gracefully declined.

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 of Taiwan].

Morris De Groot (1931-1989)

         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.

Chen Wen Chen (1950 - 1981)
Han Chinese Martyr

My 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.

Hirotugu Akaike

         Granville 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.


Granville Tunnicliffe-Wilson   Peter Green

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)

I 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.

I’m 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.

[To 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.]

I 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.)

Dennis D. Cox

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 Tim Read

Hi Tom!
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!

Tim Read
Tim 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 after.]

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 too.

I 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.

The 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.  

I 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 co-author.

         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]

In 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.

Seock-Ho Kim

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.

Kam 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 effects.

         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.]

My 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 Technometrics.

         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 different.

         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 eight-ball.

         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. 

I 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.

Josep Ginebra-Molins

         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 publicly.

         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 were.

         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 bombed.

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.

I 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.


Jon Nyquist


Dennis Kerr


In 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 well-received.

In 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 drink.”

I 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.

I 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

My 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
of experts, drug abusers, and recovering drug abusers. The recovering drug abusers were the most insightful, and they helped us
to reduce 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 methodology.

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.

The 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 rather refreshing.

         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.

Chong Gu   Michael Hamada   Taskin Atilgan
Mohammed Madi  

Linda Danielson, 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 John Hsu.

I 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 least.

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)


  © Thomas Hoskyns Leonard, 2012 - 2013