University of Plymouth PEARL https://pearl.plymouth.ac.uk 01 University of Plymouth Research Outputs University of Plymouth Research Outputs 2016-02-01 How Long Can Pope Francis Expect to Live Stander, J http://hdl.handle.net/10026.1/5417 Significance All content in PEARL is protected by copyright law. Author manuscripts are made available in accordance with publisher policies. Please cite only the published version using the details provided on the item record or document. In the absence of an open licence (e.g. Creative Commons), permissions for further reuse of content should be sought from the publisher or author. IN BRIEF STATISTICALLY SPEAKING How long can Pope Francis expect to live? He joked in 2014 that he had “two or three years left”, but that might be overly pessimistic, say Julian Stander, Luciana Dalla Valle and Mario Cortina Borja hen elected pope of and instantly became one of the most Julian Stander is period (bit.ly/1J1JV6H). Like other the Roman Catholic famous people in the world. associate professor populations, popes have experienced (reader) in mathematics Church on 13 March In August 2014, Pope Francis and statistics in the a generally increased life expectancy W2013, the Argentinian priest Jorge jokingly announced that he expected – but statistically, how many years can School of Computing, Mario Bergoglio, Archbishop of Buenos to live another two or three years, and Electronics and the present pope expect to live after Aires, took the papal name of Francis that he might even retire within this Mathematics, his election? To answer this question Plymouth University we analysed data on the post-election Luciana Dalla Valle is survival times of popes, starting with a lecturer in statistics Pope Innocent VII, whose pontificate in the School of Computing, Electronics began in 1404. and Mathematics, We arbitrarily started at the Plymouth University beginning of the fifteenth century as dates of birth, election and death (or Mario Cortina Borja is chairman of the resignation) are well documented from Significance editorial that century onwards. The resulting board, and professor data set (bit.ly/1ZSrpjt) is based on the of biostatistics in the Centre for Paediatric 62 popes before Pope Francis. Note that Epidemiology and apart from Gregory XII and Benedict Biostatistics, UCL XVI – who choose to resign the papacy Institute of Child Health in 1415 and 2013, respectively – all the popes analysed died in office. After an initial analysis of the data, we modelled ti, the post-election survival time of the i th pope in our data set, using a Weibull survival model – a common model for positive times to events. Our data included one observation that is censored – that is, the pope in question (Pope Francis’s predecessor, Pope Emeritus Benedict XVI) is still alive. Effectively, we have a lower bound on his survival. Our model also had two centred covariates: age at election (x1i) and year of election (x2i), both of which were centred by the subtraction of the sample mean. Our model took the form: trii~ Weibull( , µ ) log µi =β0 +β 11xx ii +β 22 For most popes in our data set the post- LEFT Pope Francis, election survival time is the same as pictured in November pontificate length. The exceptions are 2013, sends a kiss to Pope Gregory XII and Pope Emeritus the faithful gathered in St. Peter's Square, Benedict XVI. We performed inference neneos/iStock Editorial/Thinkstock neneos/iStock Vatican City in the Bayesian framework, and so we 12 SIGNIFICANCE February 2016 © 2016 The Royal Statistical Society IN BRIEF Election year 1750, Age at election 60 0.3 0.15 0.2 Current 0.1 Pontificate length 0.0 2.89 years Election year 1750, Age at election 80 0.3 0.10 0.2 0.1 0.0 Election year 1950, Age at election 60 Probability density Probability density 0.10 0.05 0.05 0.00 Election year 1950, Age at election 80 0.20 0.15 0.10 0.05 0.00 0.00 10 20 30 0 5 10 15 20 25 30 Median Post−Election Survival Time (years) Post−Election Survival Time (years) FIGURE 1 FIGURE 2 needed to specify prior distributions for FIGURE 1 Posterior older at the time of their election tend to about his own survival seems rather the unknown parameters in our model, distributions of the have shorter pontificates. pessimistic: based on the survival of median post-election r, β0, β1 and β2: survival time for popes Pope Francis was 76 years old when past popes, he can expect to live at elected in 1750 and elected in 2013. His pontificate has least 10 years with probability 50%, r ~ Exp rate 0.001 1950, aged 60 and 80 so far lasted 2.89 years at the time and 25 years with probability 5%. βββ, , ~N (mean = 0, variance = 10 000) 012 when elected of writing (February 2016). We can Of course, there is scope for more There was no posterior support for FIGURE 2 The understand the future survival time sophisticated analysis of papal post- an interaction term between age predictive probability tnew of a pope such as Pope Francis by election survival times. In addition, at election and year of election. density function of the considering the predictive probability similar analyses could be conducted for post-election survival Our inference is thus based on time for a pope elected density function: individuals comprising different special the posterior distribution of the in 2013, aged 76, who, populations, such as monarchs and p>ttnew | all available data, new 2.89 unknown parameters given the data: like Pope Francis, ( ) other heads of state. Note, however, that has already served (r, unless we are dealing with leaders that p β0, β1, β2 | data). We simulated 2.89 years We can use the sample from the posterior 500 000 values of r, β0, β1 and β2 from density, p(r, β0, β1 and β2 | data), have all been male, such as presidents this posterior distribution using a together with simulations from an of the United States, a covariate Markov chain Monte Carlo algorithm appropriate Weibull distribution, to indicating gender must be included. n implemented in JAGS1 using R2jags.2 generate values from this predictive Figure 1 shows posterior distributions distribution. Figure 2 shows the References of the median post-election survival predictive probability density function 1. Plummer, M. (2003) JAGS: A program for time for hypothetical popes elected in of the post-election survival time for a analysis of Bayesian graphical models using 1750 and 1950, aged 60 and 80 at the pope such as Pope Francis. The median Gibbs sampling. http://citeseer.ist.psu.edu/ time of election. The graphs suggest survival time is 10 years, with the 0.95 plummer03jags.html that, as the years have passed, the quantile being approximately 25 years. 2. Su, Y.-S. and Yajima, M. (2015) R2jags: Using median survival time has increased We therefore conclude that the R to Run “JAGS”. R package version 0.5-6. somewhat. Naturally, popes who are forecast made by Pope Francis in 2014 http://cran.r-project.org/package=R2jags February 2016 significancemagazine.com 13.