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ENDNOTES 38326. Fisher (1925), page 9. See Gelman and Robert (2013) for reflection on intemperate anti-Bayesian attitudesfrom the middle of last century. [25]27. See McGrayne (2011) for a non-technical history of Bayesian data analysis. See also Fienberg (2006),which describes (among many other things) applied use of Bayesian multilevel models in election prediction,beginning in the early 1960’s. [25]28. I borrow this phrasing from Silver (2012). Silver’s book is a well-written, non-technical survey of modelingand prediction in a range of domains. [27]29. See eobald (2010) for a fascinating example in which multiple non-null phylogenetic models are contrasted.[28]Chapter 230. Morison (1942). In addition to underestimating the circumference, Colombo also overestimated the size ofAsia and the distance between mainland China and Japan. [29]31. is distinction and vocabulary derive from Savage (1962). [29]32. I first encountered this globe tossing strategy in Gelman and Nolan (2002). Since I’ve been using it in classrooms,several people have told me that they have seen it in others places, but I’ve been unable to find a primevalcitation, if there is one. [30]33. is assumption is usually called either the principle of indifference or the principle of insufficient reason. ereis a very long history of debate over this principle, and there are numerous ways to justify it. None of these waysprovide any guarantees, because indeed no method of inference provides guarantees. [31]34. Van Horn (2003). Technically, any system with the same proportionality as probability theory will do. [37]35. ere is actually a set of theorems, the No Free Lunch theorems. ese theorems—and others which aresimilar but named and derived separately—effectively state that there is no optimal way to pick priors (forBayesians) or select estimators or procedures (for non-Bayesians). See Wolpert and Macready (1997) forexample. [40]36. is is a subtle point that will be expanded in other places. On the topic of accuracy of assumptions versusinformation processing, see e.g. Appendix A of Jaynes (1985): the Gaussian, or normal, error distributionneedn’t be physically correct in order to be the most useful assumption. [41]37. is approach is usually identified with Bruno de Finetti and L. J. Savage. See Kadane (2011) for review andexplanation. [44]38. See Berger and Berry (1988), for example, for further exploration of these ideas. [44]Chapter 339. Gigerenzer and Hoffrage (1995). [60]40. Feynman (1967) provides one the best defenses of this device in scientific discovery. [60]41. For a binary outcome problem of this kind, the posterior density is given by dbeta(p,w+1,n-w+1), wherep is the proportion of interest, w is the observed count of water, and n is the number of tosses. If you’re curiousabout how to prove this fact, look up “beta-binomial conjugate prior.” I avoid discussing the analytical approachin this book, because very few problems are so simple that they have exact analytical solutions like this. [60]42. See Ioannidis (2005) for another narrative of the same idea. e problem is almost certainly worse than thecalculation suggests, because non-significant results are filtered out of the published literature. [61]43. See Box and Tiao 1973, page 84 and then page 122 for a general discussion. [67]44. Gelman et al. 2013a page 33 comment on differences between percentile intervals and HPDIs. [67]