1,635
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Bayesian Evidence Accumulation in Experimental Mathematics: A Case Study of Four Irrational Numbers

&

References

  • [Aragón Artacho et al. 12] F. J. A. Aragón Artacho, D. H. Bailey, J. M. Borwein, and P. B. Borwein. “Walking on Real Numbers.” Math. Intell. 35 (2012), 42–60.
  • [Bailey and Borwein 09] D. H. Bailey and J. M. Borwein. “Experimental Mathematics and Computational Statistics.” Wiley Interdiscip. Rev.: Comput. Stat., 1 (2009) 12–24.
  • [Bailey et al. 12] D. H. Bailey, J. M. Borwein, C. S. Calude, M. J. Dinneen, M. Dumitrescu, and A. Yee. “An Empirical Approach to the Normality of π.” Exp. Math. 21 (2012), 375–384.
  • [Bailey and Crandall 01] D. H. Bailey and R. E. Crandall. “On the Random Character of Fundamental Constant Expansions.” Exp. Math. 10 (2001) 175–190.
  • [Berger and Berry 88a] J. O. Berger and D. A. Berry. “The Relevance of Stopping Rules in Statistical Inference.” Statistical Decision Theory and Related Topics, vol. 4, edited by S. S. Gupta and J. O. Berger, pp. 29–72. New York: Springer Verlag, 1988a.
  • [Berger and Berry 88b] J. O. Berger and D. A. Berry. “Statistical Analysis and the Illusion of Objectivity.” Am. Sci. 76 (1988b) 159–165.
  • [Borel 09] E. Borel. “Les probabilités dénombrables et leurs applications arithmétiques.”, Rendiconti del Circolo Matematico di Palermo (1884--1940) 27 (1909), 247–271.
  • [Borel 65] E. Borel, editor. Elements of the Theory of Probability. Englewood Cliffs, NJ: Prentice-Hall, 1965.
  • [Borwein et al. 04] J. M. Borwein, D. H. Bailey, and D. Bailey. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Natick, MA: AK Peters, 2004.
  • [Dalal and Hall 83] S. R. Dalal and W. J. Hall. “Approximating Priors by Mixtures of Natural Conjugate Priors.” J. Royal Stat. Soc. Ser. B. (Methodol.) 45 (1983), 278–286.
  • [Frey 09] J. Frey. “An Exact Multinomial Test for Equivalence.” Can. J. Stat./La Revue Canadienne de Statistique 37 (2009), 47–59.
  • [Frühwirth–Schnatter 06] S. Frühwirth–Schnatter. Finite Mixture and Markov Switching Models. New York: Springer, 2006.
  • [Ganz 14] R. E. Ganz. “The Decimal Expansion of π Is Not Statistically Random.” Exp. Math. 23 (2014), 99–104.
  • [Jaditz 00] T. Jaditz. “Are the Digits of π an Independent and Identically Distributed Sequence?” Am. Stat. 54 (2000), 12–16.
  • [Jeffreys 61] H. Jeffreys. Theory of Probability. Third edition. Oxford, UK: Oxford University Press, 1961.
  • [Kass and Raftery 95] R. E. Kass and A. E. Raftery. “Bayes Factors.” J. Am. Stat. Assoc. 90 (1995), 773–795.
  • [Lindley 57] D. V. Lindley. “A Statistical Paradox.” Biometrika, 44 (1957) 187–192.
  • [Marsaglia 05] G. Marsaglia.,“On the Randomness of pi and Other Decimal Expansions.” Interstat 5 (2005).
  • [O’Hagan and Forster 04] A. O’Hagan and J. Forster. Kendall’s Advanced Theory of Statistics, Vol. 2B: Bayesian Inference. Second edition. London: Arnold, 2004.
  • [Polya 41] G. Polya. “Heuristic Reasoning and the Theory of Probability.” Am. Math. Month. 48 (1941), 450–465.
  • [Ramsey 26] F. P. Ramsey. “Truth and Probability.” In: The Foundations of Mathematics and Other Logical Essays edited by R. B. Braithwaite, pp. 156–198. London: Kegan Paul, 1926.
  • [Spiegelhalter et al. 94] D. J. Spiegelhalter, L. S. Freedman, and M. K. B. Parmar. “Bayesian Approaches to Randomized Trials (with discussion).” J. Royal Stat. Soc. A 157 (1994), 357–416.
  • [Tu and Fischbach 05] S.-J. Tu and E. Fischbach. “A Study on the Randomness of the Digits of π.” Int. J. Mod. Phys. C. 16 (2005) 281–294.
  • [Venn 88] J. Venn.The Logic of Chance. Third edition. New York: MacMillan, 1888.
  • [Wrench Jr 60] J. W. Wrench Jr. “The Evolution of Extended Decimal Approximations to π.” Math. Teach. 53 (1960), 644–650.
  • [Wrinch and Jeffreys 21] D. Wrinch and H. Jeffreys. “On Certain Fundamental Principles of Scientific Inquiry.” Philos. Mag. 42 (1921), 369–390.