Journal of Statistical Planning andInference 113 (2003) 371–374

www.elsevier.com/locate/jspi

Discussion

Tides of change: is Bayesianism the newparadigm in statistics?

Greg Wilson ∗

Statistical Sciences Group, Decision Applications Division, Los Alamos National Laboratory,P.O. Box 1663, Los Alamos, NM MS F600, 87544, USA

Abstract

For the last 50 years Bayesians and frequentists have disputed the appropriate way to dostatistics. Bayesian methods have grown in popularity and acceptance, but how is the con1ictbetween Bayesians and frequentists likely to play out in the future? This article uses theoriesadvanced by Thomas Kuhn and Lawrence Grossberg to o5er a framework for understandingpossible futures and to pose questions about the future of the 6eld of statistics. Published byElsevier Science B.V.

Keywords: Bayesian; Frequentist; Paradigm

The dispute between Bayesian and frequentist statisticians has been intense andheated for the last 50 years. As we move into the new century, one might wonderhow this con1ict is going to play out. Will one side win while the other side is rel-egated to the dustbin of disciplinary history? Will the philosophical di5erences thatare held so strongly by the partisans get lost as those in the middle adopt whatevermethods get the job done? We might get an inkling of what is to come by looking atwhat some theories of disciplinary dynamics might predict.

One way to examine these questions is to utilize Thomas Kuhn’s theory of paradigmshifts. Kuhn’s book The Structure of Scienti/c Revolutions was a seminal work inthe philosophy of science, and continues to be one of the most widely assigned textsat American Universities. His theory claims that most of science and most scienti6ccareers are devoted to “normal science”. By normal science Kuhn means the mundanetask of proving the assumptions and implications of the current paradigm. When thecurrent paradigm begins to fail, when questions and anomalies arise that cannot beanswered by the paradigm, a rival paradigm is likely to arise that may come to replace

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372 G. Wilson / Journal of Statistical Planning and Inference 113 (2003) 371–374

the 1agging one. This is certainly how many Bayesians seem to think about theirrelationship to frequentism — seeing frequentism as a system that no longer adequatelyanswers the questions that face the discipline.

Since for Kuhn, both the incumbent and rival paradigm each represent a narrowand idiosyncratic worldview, their beliefs and practices tend to be mutuallyexclusive — they are signi6cantly divergent ways of understanding the world. Thequestioning of the accepted paradigm and the appearance of the rival one conse-quently causes a great sense of crisis — foundational concepts are called into questionand members of the discipline must choose between two systems of thought that arelargely contradictory. Kuhn cites historical 6gures like Copernicus, Mendel, and Darwinwho brought such crises into their 6elds. In hindsight, we view these men as vision-aries, but their scienti6c communities did not applaud them in their day. Likewise,history is probably littered with potential visionaries whose great ideas did not winout against the dominant paradigm, men and women who were shouted down byscience.

Using this theory as a lens, what then can we say about the Bayesian–frequentistcon1ict in statistical science? The concepts of subjective and objective probability cer-tainly have coexisted for centuries, but in this century frequentist statistics has heldthe upper hand, even though Bayesianism has made great gains towards acceptance asa viable way of doing statistics. We might say that subjective=objective probability orBayesianism=frequentism represent di5erent paradigms, but if we follow Kuhn’s model,that would suggest that one is on its way to “winning out” over the other.

A Bayesian statistician said to me a few months ago that Bayesian statistics hadalready won out. Acceptance of that claim would depend on how we chose to de6newinning, but an argument can be made to support the claim. Where once graduatestudents doing Bayesian dissertations were advised to try not to look too Bayesianwhen they went on the job market, now great numbers of graduate students try toinclude some Bayesian 1avor in their dissertations to increase their marketability. In-stead of splitting o5 and starting their own journals, Bayesians have successfully andextensively published in JASA and other prominent journals, bringing their methodsinto the spotlight where they cannot be ignored. Bayesians also have made strides inarticulating their methods as a more ethical approach to clinical trials and other prob-lems, and the clients of statistics (i.e., scientists, researchers, and decision makers) areincreasingly choosing Bayesian analyses. To use Kuhn’s model, perhaps Bayesianismis on its way to replacing the frequentist paradigm.

If we take Kuhn’s either=or model to be viable, then one paradigm will win andthe other will lose. Ultimately, there can be no coexistence of two systems based oncontradictory views of probability. If, however, we turn away from the zero sum gameof winners and losers, and consider the possibility that both Bayesianism and frequen-tism are viable methodological systems that will continue to thrive side by side, thenthe 6eld must sort out the implications of accepting or blending the two viewpoints.There are 5 or 6 rival paradigms that seek to explain basic human psychology (i.e.,Freudianism, behaviorism, etc.), which Kuhn regards as a sign that psychology is notmature enough as a 6eld to have found a de6nitive way to understand what it thinks.How mature is Statistical Science? Can rabid Bayesians and hardcore frequentists

G. Wilson / Journal of Statistical Planning and Inference 113 (2003) 371–374 373

accept the compromise that many self-labeled “pragmatic” statisticians have adopted,using whatever methods seem appropriate to the task at hand, whether Bayesian orfrequentist?

Although Bayesians have been successful in broadening the acceptance of their meth-ods, they have done this by demonstrating and touting the usefulness of the methods.When philosophical arguments won early Bayesians few converts, they decided to putphilosophical arguments on the back burner and get on with the research and publish-ing that they felt would show the superiority of their methods. Their methodologicalsuccesses have indeed impressed many within the 6eld and without, but those whohave adopted the Bayesian methods have often done so without adopting the Bayesianphilosophy. The question remains whether the philosophy can ever be successfully re-joined with the methods in wide use. People adopt new tools more readily than newphilosophies. Pragmatic statisticians will employ the tools that best solve problems andbest bring in grant money. Scientists who use statistics may buy into the argumentthat a Bayesian approach produces direct probabilities that are easier to describe whenwriting up the results of an experiment, but they are seldom interested in why onestatistical approach may be more philosophically correct to a statistician. In reality,pragmatic statisticians are not all that concerned with the philosophical underpinningsof the methods, happy to stipulate situationally that probability works this way or that.The partisan adherents to Bayesianism and frequentism are surely baMed by this prag-matic turn, but perhaps in science you have a choice of casualties: war guaranteesthe death of one of the combatants, and peace guarantees the death of the underlyingphilosophies that started the war in the 6rst place. It is hard to tell which way isstatistical science headed?

Another possibility might prove Bayesianism’s success to be a double-edged sword,with Bayesianism emerging not as a rival but as a set of methods to be assimilatedand subsumed by mainstream statistics. Lawrence Grossberg discusses in his book WeGotta Get Out of This Place how dominant groups de-fang the threat of potential rivalsby assimilating the alternative practices the rivals propose. The assimilation process thatGrossberg outlines begins with the dominant group repudiating the rival altogether, thendrawing boundaries that specify what parts of the rival’s practices are acceptable andwhat parts aren’t, and 6nally adopting most of the rival’s practices completely whilesaying that those practices were really a part of the dominant group’s way of doingbusiness all along.

Grossberg uses the example of the relationship of rock and roll and conservativereligious groups in the United States. Religious groups once completely repudiatedrock music, then drew boundaries, and now include Christian rock in the categoryof accepted and valued practices. We might also draw comparisons to the culturalassimilation of radical 6gures like Dr. Martin Luther King, Jr., whose virulent criticismsof American culture and government policies during the 1960s have been forgotten sothat he can now be remembered as a peaceful symbol of everything that is good aboutAmerica (while many of the social ills he criticized rage on).

Potentially, this is the future fate of Bayesianism as well. Bayesianism won’t replacefrequentism and assume the mantle of mainstream statistics — instead Bayesian meth-ods will be assimilated, and the radicalness of their challenge will be romanticized

374 G. Wilson / Journal of Statistical Planning and Inference 113 (2003) 371–374

as an example of everything that is good about frequentism. Stranger things havehappened.

How can we tell if=when Bayesianism has won? Is it enough for Bayesian methodsto be visible and viable for statisticians and scientists? Will Bayesianism succeed as amethodology and fail as a philosophy? What can the rabid Bayesians do to rejoin theirmethods and their philosophy so that acceptance of the former involves an understand-ing of the latter? And how does any of this a5ect the con6rmed frequentist? Has theinsurgence of Bayesianism been a bene6t, a threat, or a mere annoyance for them?

While it is certainly impossible to plan the evolution and development of a disciplinelike statistical science, it seems that those who have the strongest opinions about itsfuture direction are least satis6ed with its current state. It also seems that those whohave pushed hardest to develop Bayesian methods (and perhaps the same is true withthose who have pushed hardest to develop frequentist methods) are least happy withthe legacy that is forming.