Thomas Hoskyns Leonard is a Retired Professor of Statistics, formerly of the Universities of Wisconsin and Edinburgh. He studied at Imperial College and University College London from 1966-72, and from 1972-79 he taught at the University of Warwick, where he co-founded the Department of Statistics and MORSE degree with Robin Reed and P.J. Harrison.

He is a fellow of the Royal Statistical Society and a co-founder, with Arnold Zellner, of the International Society for Bayesian Analysis (ISBA). He is also a writer of fiction and a poet.

Leonard has made seminal contributions to Bayesian categorical data analysis, prior informative density estimation and function smoothing, conditional Laplacian approximations for Bayesian marginal inference and prediction, the statistical modelling of log covariance matrices, and to applications of Bayesian methodology in many areas, in particular Obstetrics and Gynaecology, and Geophysics. Most recently, he has submitted a large amount of anecdotal and statistical evidence to the Scottish Parliament regarding the widespread devastating side effects of psychiatric medications and electroconvulsive therapy.

Statistics Views interviews Professor Leonard about his career in statistics.

**1. What was it that introduced you to statistics as a discipline?**

The pure and applied mathematics courses which I studied for my undergraduate degree at Imperial College were much too difficult for a green-behind-the-ears teenager from the West Country. I however found solace in David Cox’s courses on Stochastic Processes and Statistics, and became totally convinced by his pragmatic, frequency approach to Statistics. Then, in my final year, Ann Mitchell taught an engrossing series of Statistics lectures, whilst also taking a personal interest in me and nurturing my interest in the subject. So, I suppose that I became a statistician by default. The pure and applied mathematicians at Imperial College seemed to be teaching almost everything else in a quite obscure, unintelligible, and élitist fashion, though that may just have been my perception of them!

**2. You’ve taught at a variety of institutions around the world. How did your teaching and research motivate and influence each other?**

My Statistics 775 course on Bayesian Decision theory at the University of Wisconsin-Madison was extremely influential both in terms of my students’ doctoral research, and my own research. I, for example, tried to take the students working on smoothing splines and the elicitation of prior distributions to the cutting edge of their research areas. Subsequently, distinguished statisticians learnt a large component of their Bayesian skills from Statistics 775 including Wing Wong, James and Joanne Wendelberger, Michael Hamada, Finbarr O’Sullivan, Doug Nychka, Dennis Lin, Jun Shao, and Sharon Lohr.

My interactions with my 775 students also encouraged my own research. For example, during the early 1980s, we developed and validated an alternative to expected utility which puts a positive premium on the certain components of random monetary rewards.

I also taught the interdisciplinary advanced undergraduate course Statistics 431 at Wisconsin, and here the practical projects were of essential importance. The students were encouraged to use logistic regression and Goodman’s full interaction analysis to discover new knowledge within their own disciplines. The practical developments in turn influenced my philosophies about theoretical research and its practical context and socio-scientific background.

**3. The late Professor Dennis Lindley was your PhD supervisor. What are your memories when you look back on being taught by Lindley? Was that a golden age for Bayesian Statistics?**

My Ph.D. supervisor Dennis Lindley was a quintessential and quite deductive mathematical statistician of the old school with condescending opinions about ‘mere data analysis’. I, in contrast, have always thought in more inductive and pragmatic fashion. While he was an extremely charming gentleman, Dennis always told me what to think, and that would invariably be from his highly individualistic, prescriptive, coherently conjugate Bayesian viewpoint. As I was an insecure and quite neurotic young man, that damaged my self-credibility and put me in a state close to mystification, for example during the stern lecture I received after saying ‘But, Dennis, we can have our cake and eat it. We can assume this hierarchical prior distribution for my logits, and then estimate our prior parameters from the data’.

When I was writing up my very first paper, for *Biometrika*, Dennis advised me ‘Tell the readers what you’re going to say, say it, and then tell them what you’ve said.’ David Cox, as editor of *Biometrika*, shortened my manuscript by about two thirds.

While the early 1970s were projected, by some, as the Golden Age of Bayesian Statistics, this conclusion was based on the false premise that everybody else was wrong. It is only more recently, as we continue to blend together the Bayesian, frequency, and pragmatic approaches to statistical inquiry that we are beginning to achieve the sort of socio-scientific credibility which might justify a description of this type.

**4. In December 2012, you were elected as one of the first ever Fellows of the International Society for Bayesian Analysis, which you founded with Arnold Zellner. Why did you feel a society for Bayesian Analysis was needed? How has the Society developed over the years, and responded to the changing needs of the statistical community?**

Arnold Zellner and I felt that a Bayesian Society like ISBA was needed partly to broaden the paradigm away from the élitist schools with their special agendas, but primarily to emphasise the interdisciplinary nature of the Bayesian paradigm and to enhance our links with as many subject areas as possible. Some of the British Bayesians were initially quite reluctant to join in, but nowadays, distinguished Bayesians are appearing out of the woodwork from a good many disciplines and from almost every country in the world. For example, Carlos Pereira and his fellow Bayesians in Brazil are very influential in scientific and social terms, and the Bayesians in India, Italy, Germany, Greece and Norway are producing some fine theoretical and practical work. ISBA has got into electronic communication in a big way, and their journal *Bayesian Analysis *is very widely and beneficially read. The recent advances in Machine Learning and Political Science owe much, for example, to this interaction.

**5. You are also a Fellow of the Royal Statistical Society. The getstats campaign by the Royal Statistical Society focuses on improving the public’s understanding of statistics in every-day life. Do you think that the public’s understanding of statistics has improved in recent years? What can be done to improve it further?**

I think that the general public understand the statistics which are meted out to them by the Establishment all too well i.e. statistics are very often politically motivated and all too often quite misleading. Indeed, too much emphasis is placed on classical *p*-values which do not actually measure practical significance, and many apparent correlations can be made spurious by the presence of confounding variables. Data is sometimes even rearranged or shuffled, or important variables omitted, to give appropriately optimistic projections. ‘Evidence-based conclusions‘ based on observational data and non-randomised experiments often turn out to be ‘spuriously evidence-based’. I refer, for example, to Jim and Margaret Cuthbert’s splendid presentation during the Royal Statistical Society’s recent debate in Edinburgh on the Statistics of the Referendum.

I believe that most statistical investigations are inherently subjective in nature, and that statisticians should no longer attempt to achieve ‘false objectivity’. Rather than attempting to educate the public in a possibly misleading manner, I think that our leading statistical societies should focus on encouraging their members to invariably insist on fairness, professionalism, and impartial honesty, while acknowledging the subjective nature of their conclusions. It is only then that we can hope to properly educate the public regarding the real benefits that can be gained from statistical investigations.

The Royal Statistical Society has of course made some wonderful attempts to educate the public in their magazine *Significance*. However, one of my non-statistical friends who reads my copies of *Significance *remains quite cynical. He indeed wonders whether statistics can do much more than reiterate the obvious.

I believe that most statistical investigations are inherently subjective in nature, and that statisticians should no longer attempt to achieve ‘false objectivity’. Rather than attempting to educate the public in a possibly misleading manner, I think that our leading statistical societies should focus on encouraging their members to invariably insist on fairness, professionalism, and impartial honesty, while acknowledging the subjective nature of their conclusions. It is only then that we can hope to properly educate the public regarding the real benefits that can be gained from statistical investigations.

**6. At the recent Future of Statistical Sciences workshop, there was much talk about Big Data and a concern that many ‘hot areas’ such as big data/data analytics, which have close connections with statistics and the statistical sciences, are being monopolised by computer scientists and/or engineers. What do statisticians need to do to ensure their work and their profession get noticed?**

Large scale number crunching is unlikely to work well in any truly meaningful sense without careful statistical and scientific interpretation of what is going on in relation to the real-life background of the data, and to any supplementary anecdotal evidence which may be at hand. For their work and their profession to get noticed, statisticians simply need to do their job properly by, for example, combining anecdotal evidence with the information in the numerical data.

**7. Is there a particular piece of work (research or otherwise) that you are proudest of?**

I am proudest of my paper with John Hsu on Bayesian Inference for a Covariance Matrix, which appeared in the *Annals of Statistics* in 1992. We employed a multivariate normal prior distribution, for the upper triangular elements of the matrix logarithm of a multivariate normal covariance matrix, and used some highly complex Volterra equation techniques from Mathematical Physics to complete the prior to posterior analysis.

I’d published my much simpler solution in the special case where the sample covariance matrix is diagonal in *Technometrics *in 1975, and this was subsequently extended by Daniel Gianola and his co-authors and applied to Animal Breeding.

In my 1996 paper with Tom Chiu and Kam-Wah Tsui in the *Journal of the American Statistical Association*,we extended some of the ideas in my 1992 paper to an analysis of a ‘Matrix Logarithmic Covariance Model’. Since then, all these ideas have been beneficially employed by a number of authors in *Econometrics*, including James Le Sage, Kelley Pace and Manabu Asai, for example to spatial processes and to multivariate time series models for the analysis of stochastically volatile data.

**8. What has been the best book on statistics that you have ever read?**

*Optimal Statistical Decisions* by Morris De Groot is the highest quality statistics book that I have ever read. De Groot was a key figure in the history of Bayesian Statistics and a scientist of enormous stature.

**9. Do you think over the years too much research has focussed on less important areas of statistics? Should the gap between research and applications get reduced? How so and by whom?**

I believe in the Wisconsin philosophy of ‘winnowing and sifting’. In academia, all sorts of research should be encouraged, and even the zaniest of conclusions entertained, since this maintains unconstrained creativity of the scientific process. However, at the winnowing and sifting stage, it is the practical applicability of the academic conclusions which is of primary importance. If we proscribe too much regarding our research programs, then we will limit creativity, and thereby reduce the potential applicability of our discovery process.

**10. What do you see as the greatest challenges facing the profession of statisticians in the coming years?**

We have always needed to emphasise that statistics is not just a branch of mathematics, since inductive reasoning in relation to the data and its socio-scientific background is also of essential importance. The main challenge to statistics groups which are part of a Mathematics department is for the groups to maintain their independent, well-valued identities. Statisticians are more generally faced with the challenge as to where to house themselves, since our profession is becoming increasingly interdisciplinary in nature, and more and more experts in other areas are imagining that they are also experts in statistics.

**11. If you had not got involved in the field of statistics, what do you think you would have done? (Is there another field that you could have seen yourself making an impact on?)**

As I was good at mathematics, which I found to be quite boring, I was channelled into the science stream at my high school and encouraged to study for Physics and Chemistry at A-level, together with Maths and Further Maths, instead of the History and English literature that I was really interested in. If I had been allowed to study English literature, then I may well have become a novelist and poet instead of a statistician. Now, fifty years later, I am working on being just that. For example, my poems ‘The Bayesians of Auld Edinburgh’ and ‘Wherefore Dennis?’ are appended to my personal history of Bayesian Statistics. I have self-published two novels on my website, and I have recently completed the first three chapters of *A Devonian Saga*, a murder and family ancestry mystery set during my teenage years in Plymouth.