aa r X i v : . [ s t a t . M E ] M a y Statistical Science (cid:13)
Institute of Mathematical Statistics, 2014
Contribution by M. A. Girolami
Mark A. Girolami
This collection of Big Bayes Stories could be parti-tioned into two groups, one relating to the sciences,cosmology in particular, and the other relating topublic policy, that is, health, fisheries managementand demographics.My first comment here is that inferential issues re-lated to the sciences and the shaping and guiding ofpublic policies can only be addressed appropriatelyby adoption of the Bayesian framework. This is avery strong, and no doubt provocative, statement,the opinion of which has been formed by my ownexperience of working very closely with a range ofbasic scientists, clinical professionals and econome-tricians providing support in developing fiscal pol-icy.The almost wholesale adoption of the Bayesianframework by astronomers and cosmologists is agood case in point where subjective Bayesian infer-ence is viewed as a formal codification of the scien-tific method and therefore most natural in guidingscientific inquiry.I have had first-hand experience of this whenworking with cellular biologists who previously hadviewed statistical analysis as the means of provid-ing nothing more than the p -values required bythe editors of journals such as Nature . However,when presented with the Bayesian formalism of anexpert informed prior to posterior belief updatingthe paradigm has been embraced wholeheartedly by
Mark A. Girolami is Professor, EPSRC EstablishedCareer Research Fellow, Chair of Statistics, Departmentof Statistics, University of Warwick, Coventry, CV47AL, United Kingdom e-mail: [email protected].
This is an electronic reprint of the original articlepublished by the Institute of Mathematical Statistics in
Statistical Science , 2014, Vol. 29, No. 1, 97. This reprintdiffers from the original in pagination and typographicdetail. cellular biologists and formsthe common languageof scientific collaboration, for example, Xu et al.(2010).My second comment is that many of the cases pre-sented required a complex statistical model, whichof course brings with it associated technical is-sues, but are most naturally accommodated in theBayesian framework. When considering the issues ofsystematically integrating diverse data sources, ex-ploiting model structure to employ sparse measure-ments, or formally and explicitly quantifying uncer-tainty induced due to the use of complex computercodes, it is hard to see how satisfactory and trans-parent non-Bayesian solutions would follow.In summary, I have viewed these interesting casestudies from the perspective of how feasible the re-quired analysis would be as part of an ongoing dia-logue between statisticians and scientists or statisti-cians and policy makers. All of them suggest to methat, to misquote Karl Pearson, Bayesian inferenceprovides the “Grammar of Science.”REFERENCE
Xu, T.-R. , Vyshemirsky, V. , Gormand, A. , vonKriegsheim, A. , Girolami, M. , Baillie, G. S. , Ket-ley, D. , Dunlop, A. J. , Milligan, G. , Houslay, M. D. and
Kolch, W. (2010). Inferring signaling pathway topolo-gies from multiple perturbation measurements of specificbiochemical species.
Science Signal ra20.ra20.