Stanford's star of statistical inference: a Q&A with Bradley Efron

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Bradley Efron is the Max H Stein Professor of Statistics and Biostatistics at Stanford University’s School of Humanities and Sciences and the Department of Health Research and Policy with the School of Medicine. He has worked at Stanford since earning his doctorate in statistics there in 1964 and is best known for his introduction of the bootstrap method of statistical inference.

This year, Efron has been named as the recipient of the Royal Statistical Society's highest honour, the Guy Medal in Gold. The award, which is only bestowed every three years, was made in recognition of his seminal contributions to many areas of statistics, including empirical Bayes analysis, the analysis of survival data, applications of differential geometry to statistical theory and analysis of multiple testing problems in inference for gene expression data. He has won numerous other honours recognising his contributions to theoretical and applied statistics, including the US National Medal of Science.

StatsLife caught up with the past president of the American Statistical Association and the Institute of Mathematical Statistics, prior to him travelling to the UK to receive his award, which is being formally presented at the Society's conference this September.

Did you have any idea at the time of working on the bootstrap method of statistical inference that it would come to be so widely used?

No, the bootstrap work seemed awfully simple by the time it was done, and proved a great over-achiever in terms of response. Most of the time things go the other way, where my earth-shaking ideas seem to fall upon fallow ground.

Another widely cited area of your work is empirical Bayes analysis. What do you make of the rise and rise in Bayesian statistics in recent decades? Do you think it is used too much?

I've been thinking about the Bayesian revival lately, especially as it involves objective ('uninformative') prior distributions. These are actually the dominant form of current Bayes applications. Such applications are difficult to justify on either pure Bayes or frequentist grounds, making them a fertile target for further development (in fact I have a paper scheduled to appear in JRSS-B (the Journal of the Royal Statistical Society Series B) titled 'frequentist properties of Bayesian estimates', concerning a small corner of the question).

I wouldn't say there are too many Bayesian applications, but sometimes there is too little thought given to the choice of prior.

You have been at Stanford for more than 50 years – how has the statistics department there changed over the years?

When I got to Stanford the faculty included Stein, Chernoff, Parzen, Lincoln Moses, Rupert Miller, Ingram Olkin and other stars. It was mainly a math stat stronghold, except in the medical school where Moses, Miller, and Byron Brown were practicing Fisherians. The department has changed with the profession. The math part of math stat is less in evidence, replaced with high-level methodology aimed at big data applications. It's hard to beat the line-up from 50 years ago, but the current faculty is right up there.

One big change: I was the youngest faculty member, now I'm the oldest...

Which statisticians do you most admire and why?

Let me change 'admired' to the less subjective 'influenced by'. Fisher and Neyman founded the modern discipline, and in my case Fisher's work has been particularly inspiring. Many years ago I made a mental list of the post-war statisticians of especial influence on me, Stein, Robbins, Rao, Tukey, and Cox, and that list still looks pretty good. More recently, Benjamini and the Stanford triumvirate of Hastie, Tibshirani, and Friedman have dragged me into the computer age. I'm not really fluent in computerese, but at least I can keep up with the conversation.

What inspired you to invent the Efron dice?

My first wife and I were taking an auto trip through Victoria Island. It's a beautiful place but big enough to make the automobile time stretch on a bit. I started thinking about Steinhaus' paradox of the three probability distributions that are mutually non-dominating, and thought that it would be fun to make dice illustrating the principle. Four was an easy number of dice to handle mentally. Later, my wife even made me a beautiful set of the dice, which still sits on my office shelf. I was sorry to see that my clever name 'Paradice' never caught on. What did catch on was the chance to win money on bar bets, which seems to be their main application. Warren Buffet likes to use the dice to make some point in his speeches, but so far I haven't received a billion dollars in the mail.

With increasing amounts of data at our fingertips, do you think there’s more that statistical theory could do to make use of it?

As they say on celebrity talk shows, I'm writing a book on that subject. The working title is 'Computer-age statistical inference'. What I would like to do is show how the dizzying increase in both the amount of data and the computer power to work with it is changing inference (as opposed to changing our methodology.) We need some more Fishers and Neymans to put the new methodology - boosting, random forests, the lasso, MCMC etc - into a clear theoretical framework. I'm sure the profession will get there sooner or later, but sooner would be better.

Are you happy to be named the recipient of this year's Guy Medal in Gold?

Yes indeed, and not least because it comes from the Royal Statistical Society. The RSS has overseen a significant portion of the enormous progress that statistics has made in the near century and a quarter since the Medal was initiated. So I consider this a real honour, with an English 'u' in it.

RSS Honours

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