May 15, 2017

XL-Files: Bayesian, Fiducial and Frequentist: BFF4EVER

Xiao-Li Meng writes:

I always enjoy making new friends, but I didn’t know the acronym “BFF” until June 17, 2014, when I attended ICSA-KISS Applied Statistical Symposium (acronym wisely avoided) in Portland, OR. A group of us got together after presenting and attending talks on distributional inferences because of our closely related topics: Confidence Distribution (Min-ge Xie of Rutgers), Generalized Fiducial Inference (Jan Hannig of UNC; Thomas Lee of UC Davis), Inferential Model (Ryan Martin of NC State), Objective Bayes (Dongchu Sun of Missouri), and Individualized Inference (my student Keli Liu, now at Stanford, and myself). Our shared interests motivated us to contemplate an annual workshop to explore foundational issues that are at the core of statistics as a vital underpinning of data science. Identifying a venue and funding source turned out to be easy thanks to Dongchu’s connections with East China Normal University (ECNU). But it took a bit longer to come up with a crisp title. “Well, we want to connect Bayesian, Fiducial and Frequentist, so BFF,” I was mumbling, “but what’s that?” “Oh, my younger son talks about BFF all the time,” Min-ge exclaimed, “That stands for Best Friends Forever!

The rest is happy history. After the appetizing BFF1 (November 10–14, 2014: http://www.bayes.ecnu.edu.cn/BFF2014/) and BFF2 (July 4–5, 2015: http://www.bayes.ecnu.edu.cn/BFF2015/) both at ECNU, BFF3 (April 11–13, 2016: http://stat.rutgers.edu/bff2016) took place at Rutgers. The hosts, Regina Liu and Min-ge, served a delicious full course. Keynote speakers included Jim Berger, David Cox, Brad Efron and Nancy Reid. All household names for sure, but can you guess their BFF identities (hint: some are bi-inferential)? With the blessing of these preeminent leaders, and many penetrating presentations from researchers of almost every generation, BFF3 showcased the broad and deep interests in statistical principles and foundations.

Greatly encouraged, and with tremendous help from the expanded BFF community and my multi-talented student Robin Gong and assistant Madeleine Straubel, I carried on the BFF torch. BFF4 (May 1–3, 2017: https://statistics.fas.harvard.edu/bff4) took place at Harvard, with six featured discussion sessions pairing statisticians with philosophers, computer scientists, probabilists, etc., three featured panels, and 15 invited talks. A common theme of many presentations was to explore different constructions of probability, with the goal of producing probabilities that will be most useful for scientific investigations and decision-making.

The opening session featured Art Dempster and Glenn Shafer—yes, as in Dempster–Shafer Theory. Art’s talk, “What Bayes Did and What Bayes Did Not Do” was meant to stimulate, but Glenn’s discussion was even more provocative: “Dempster–Shafer is Fiducial…and so are you.” Glenn argued that use of any kind of probability involves making a “fiducial move,” i.e., to intentionally ignore some relevant but hard-to-use information. Art, however, felt that Glenn’s notion of “fiducial” differs from R.A. Fisher’s original intent, however that was (un)defined.

This was just one of many thought-provoking exchanges that occurred during the opening and other featured discussions: “Using Rates of Incoherence to Refresh some old ‘Foundational’ Debates” by philosopher Teddy Seidenfeld, who was challenged by Christian Robert; “BFF Four—Are We Converging?” by Nancy Reid, with scrutiny from philosopher Deborah Mayo; “Randomisation isn’t perfect but doing better is harder than you think” by Stephen Senn, expanded upon by philosopher Ned Hall; and “Modeling Imprecise Degrees of Belief” by philosopher Susanna Rinard, with questions from Andrew Gelman.

One featured session that invoked no debate was Sandy Zabell’s fascinating account of “The Secret Life of I.J. Good,” which reasoned that Good became an important Bayesian of the twentieth century because his work with Alan Turing on Bayesian methods had played a decisive role in cracking the Enigma code. The discussant, Cynthia Dwork, a leading computer scientist on differential privacy, gave an equally fascinating account on the evolution of cryptographic research, and how it informs the development of data privacy research today.

The animated discussions continued in the three panels: “Views from Rising Stars” (Robin, Jan, Keli, Ryan, and Tyler VanderWeele), led by Pierre Jacob; “Perspectives of the Pioneers” (Jim Berger, Larry Brown, David Cox, Don Fraser, and Nancy Reid), moderated by Vijay Nair; and “Scientific Impact of Foundational Thinking” (Emery Brown, Paul Edlefsen, Andrew Gelman, Regina Liu, and Don Rubin), chaired by Min-ge.

Of course, such a richly historical (and historic) workshop would be incomplete without a banquet speech by Steve Stigler, who declared that conducting any kind of BFF inference is a “Risky Business.” But if you, too, are of the adventurous kind, please join BFF5 at University of Michigan in Ann Arbor in May 2018 (contact Peter Song at pxsong@umich.edu), so we can be best friends forever!

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