A Statistically Significant Future for Bayes' Rule

Abstract

B. Efron's entertaining Perspective “Bayes' theorem in the 21st century” (7 June, p. [1177][1]) on the past and possible future of the use of Bayes' theorem in statistical inference strategically avoids addressing the use of statistics by nonstatisticians. Unlike most professional statisticians, many empirical scientists are not able to use the method of analysis that best fits their particular problem. In addition, their understanding of the frequentist statistics in which they have been trained has been widely found to be rather abysmal. As John Tukey said in 1964, “Most uses of the classical tools of statistics have been, are, and will be, made by those who know not what they do” ([ 1 ][2]). This situation has led many to argue for an educational reform in statistical training for empirical scientists, and for increased emphasis on translating between frequentist and Bayesian measures of evidence ([ 2 ][3]). Tentative implementations of both of these projects already exist ([ 2 ][3]), and these attempts merit encouragement and praise, all the more because Bayesian statistics is proving to be particularly useful in many fields. Reasons for this increased popularity in Bayesian methods are not hard to spot. Much of modern research, particularly in the life sciences, is based on the synthesis of multiple categories of evidence. Data coming from many different studies have to be integrated in order to assess the empirical evidence for a new theory, and Bayesian statistics lends itself very well to this. Working scientists have noticed this, and many are using these tools now. With the increasing statistical literacy of empirical scientists and the growing availability of Bayesian computer software, the future of Bayes' rule, along with that of other approaches to inference, seems well assured. 1. [↵][4] 1. J. W. Tukey , Am. Stat. 19, 23 (1965). [OpenUrl][5][CrossRef][6][Web of Science][7] 2. [↵][8] 1. S. Greenland, 2. C. Poole , Epidemiology 24, 62 (2013). [OpenUrl][9][CrossRef][10][PubMed][11][Web of Science][12] [1]: http://www.sciencemag.org/content/340/6137/1177.full [2]: #ref-1 [3]: #ref-2 [4]: #xref-ref-1-1 View reference 1 in text [5]: {openurl}?query=rft.jtitle%253DAm.%2BStat.%26rft.volume%253D19%26rft.spage%253D23%26rft_id%253Dinfo%253Adoi%252F10.2307%252F2682374%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [6]: /lookup/external-ref?access_num=10.2307/2682374&link_type=DOI [7]: /lookup/external-ref?access_num=A1965CDG0900002&link_type=ISI [8]: #xref-ref-2-1 View reference 2 in text [9]: {openurl}?query=rft.jtitle%253DEpidemiology%26rft.volume%253D24%26rft.spage%253D62%26rft_id%253Dinfo%253Adoi%252F10.1097%252FEDE.0b013e3182785741%26rft_id%253Dinfo%253Apmid%252F23232611%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [10]: /lookup/external-ref?access_num=10.1097/EDE.0b013e3182785741&link_type=DOI [11]: /lookup/external-ref?access_num=23232611&link_type=MED&atom=%2Fsci%2F341%2F6144%2F343.1.atom [12]: /lookup/external-ref?access_num=000312498600009&link_type=ISI