(The following is our preface to the incoming “Big Bayes stories” special issue of Statistical Science, edited by Sharon McGrayne, Kerrie Mengersen and myself.)
Bayesian statistics is now endemic in many areas of scienti c, business and social research. Founded a quarter of a millenium ago, the enabling theory, models and computational tools have expanded exponentially in the past thirty years. So what is it that makes this approach so popular in practice? Now that Bayesian statistics has “grown up”, what has it got to show for it- self? In particular, what real-life problems has it really solved? A number of events motivated us to ask these questions: a conference in honour of Adrian Smith, one of the founders of modern Bayesian Statistics, which showcased a range of research emanating from his seminal work in the field, and the impressive book by Sharon McGrayne, the theory that would not die. At a café in Paris in 2011, we conceived the idea of gathering a similar collection of “Big Bayes stories”, that would demonstrate the appeal of adopting a Bayesian modelling approach in practice. That is, we wanted to collect real cases in which a Bayesian approach had made a significant di fference, either in addressing problems that could not be analysed otherwise, or in generating a new or deeper understanding of the data and the associated real-life problem.
After submitting this proposal to Jon Wellner, editor of Statistical Science, and obtaining his encouragement and support, we made a call for proposals. We received around 30 submissions (for which authors are to be warmly thanked!) and after a regular review process by both Bayesian and non-Bayesian referees (who are also deeply thanked), we ended up with 17 papers that reflected the type of stories we had hoped to hear. Sharon McGrayne, then read each paper with the utmost attention and provided helpful and encouraging comments on all. Sharon became part the editorial team in acknowledgement of this substantial editing contribution, which has made the stories much more enjoyable. In addition, referees who handled several submissions were asked to contribute discussions about the stories and some of them managed to fi nd additional time for this task, providing yet another perspective on the stories..
| Bayesian Estimation of Population – Level Trends in Measures of Health Status |
Mariel M. Finucane, Christopher J. Paciorek, Goodarz Danaei, and Majid Ezzati |
| Galaxy Formation: Bayesian History Matching for the Observable Universe |
Ian Vernon, Michael Goldstein, and Richard G Bower |
| Estimating the Distribution of Dietary Consumption Patterns |
Raymond James Carroll |
| Bayesian Population Projections for the United Nations |
Adrian E. Raftery, Leontine Alkema, and Patrick Gerland |
| From Science to Management: Using Bayesian Networks to Learn about Lyngbya |
Sandra Johnson, Eva Abal, Kathleen Ahern, and Grant Hamilton |
| Search for the Wreckage of Air France Flight AF 447 |
Lawrence D Stone, Colleen M. Keller, Thomas M Kratzke, and Johan P Strumpfer |
| Finding the most distant quasars using Bayesian selection methods |
Daniel Mortlock |
| Estimation of HIV burden through Bayesian evidence synthesis |
Daniela De Angelis, Anne M Presanis, Stefano Conti, and A E Ades |
| Experiences in Bayesian Inference in Baltic Salmon Management |
Sakari Kuikka, Jarno Vanhatalo, Henni Pulkkinen, Samu Mäntyniemi, and Jukka Corander |
As can be gathered from the table of contents, the spectrum of applications ranges across astronomy, epidemiology, ecology and demography, with the special case of the Air France wreckage story also reported in the paper- back edition of the theory that would not die. What made those cases so well suited for a Bayesian solution? In some situations, the prior or the expert opinion was crucial; in others, the complexity of the data model called for a hierarchical decomposition naturally provided in a Bayesian framework; and others involved many actors, perspectives and data sources that only Bayesian networks could aggregate. Now, before or (better) after reading those stories, one may wonder whether or not the “plus” brought by the Bayesian paradigm was truly significant. We think they did, at one level or another of the statistical analysis, while we acknowledge that in several cases other statistical perspectives or even other disciplines could have brought another solution, but presumably at a higher cost.
Now, before or (better) after reading those stories, one may wonder whether or not the \plus” brought by the Bayesian paradigm was truly signifi cant. We think it did, at one level or another of the statistical analysis, while we acknowledge that in several cases other statistical perspectives or even other disciplines could have provided another solution, but presumably at a higher cost. We think this collection of papers constitutes a worthy tribute to the maturity of the Bayesian paradigm, appropriate for commemorating the 250th anniversary of the publication of Bayes’ Essay towards solving a Problem in the Doctrine of Chances. We thus hope you will enjoy those stories, whether or not Bayesiana is your statistical republic.
While I was trying to find a proper window to take a picture of the mountains of Eastern Turkey, an Air France flight attendant suggested me to try the view from the pilots’ cockpit! I thought she was joking but, after putting a request to the captain, she came to walk me there and I had a fantastic five minutes with the pilots, chatting and taking unconstrained views of the region of Van, as we were nearing Turkey. I was actually most surprised at the very possibility of entering the cockpit as I thought it was now completely barred to passengers. Thanks then to the Air France crew that welcomed me there!
Deborah Mayo wrote a 
