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250 Statistics’ two theoriesAcknowledgmentThis research was funded in part by the Natural Sciences and Engineering ResearchCouncil of Canada, by the Senior Scholars Funding at York University,and by the Department of Statistical Sciences at the University of Toronto.Thanks to C. Genest and A. Wang for help in preparing the manuscript.ReferencesAbraham, C. (2009). Vioxx took deadly toll study. Globe and Mailhttp://www.theglobeandmail.com/life/study-finds-vioxx-tookdeadly-toll/article4114560/Barndorff-Nielsen, O.E. and Cox, D.R. (1994). Inference and Asymptotics.Chapman & Hall, London.Bayes, T. (1763). An essay towards solving a problem in the doctrine ofchances. Philosophical Transactions of the Royal Society, London,53:370–418.Bergin, C. (2007). Remembering the mistakes of Challenger.nasaspaceflight.com.Bernardo, J.M. (1979). Reference posterior distributions for Bayesian inference.Journal of the Royal Statistical Society, Series B, 41:113–147.Box, G.E.P. and Cox, D.R. (1964). An analysis of transformations (withdiscussion). Journal of the Royal Statistical Society, Series B, 26:211–252.Brazzale, A.R., Davison, A.C., and Reid, N.M. (2007). Applied Asymptotics.Cambridge University Press, Cambridge, UK.Dalai, S. and Fowlkes, B. (1989). Risk analysis of the space shuttle: Pre-Challenger prediction of failure. Journal of the American Statistical Association,84:945–957.Davison, A.C., Fraser, D.A.S., Reid, N.M., and Sartori, N. (2014). Accuratedirectional inference for vector parameters. Journal of the AmericanStatistical Association, to appear.Dawid, A.P., Stone, M., and Zidek, J.V. (1973). Marginalization paradoxes inBayesian and structural inference. Journal of the Royal Statistical Society,Series B, 35:189–233.