Project Euclid

References

• [1] Aalen, O., Andersen, P. K., Borgan, Ø., Gill, R. and Keiding, N. (2009). History of applications of martingales in survival analysis. Electronic J. History Probab. Statist. 5. Available at www.jehps.net.
• [2] Abramowitz, M. and Stegun, I. A., eds. (1964). Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables. US Government Printing Office, Washington, DC.
  Mathematical Reviews (MathSciNet): MR167642
  
• [3] Aldrich, J. P-value and prob-value. Earliest Known Uses of Some of the Words of Mathematics. Available at jeff560. tripod.com/p.html.
• [4] Anscombe, F. J. (1954). Fixed-sample-size analysis of sequential observations. Biometrics 10 89–100.
• [5] Apostol, T. M. (1999). An elementary view of Euler’s summation formula. Amer. Math. Monthly 106 409–418.
  Mathematical Reviews (MathSciNet): MR1699259
  Digital Object Identifier: doi:10.2307/2589145
  JSTOR: links.jstor.org
  
• [6] Armitage, P. (1961). Discussion of “Consistency in statistical inference and decision,” by C. A. B. Smith. J. Roy. Statist. Soc. Ser. B 23 30–31.
  Mathematical Reviews (MathSciNet): MR124097
  JSTOR: links.jstor.org
  
• [7] Bernardo, J. M. and Smith, A. F. M. (2000). Bayesian Theory. Wiley, Chichester.
  Mathematical Reviews (MathSciNet): MR1274699
  
• [8] Bienvenu, L., Shafer, G. and Shen, A. (2009). On the history of martingales in the study of randomness. Electronic J. History Probab. Statist. 5. Available at www.jehps.net.
  Mathematical Reviews (MathSciNet): MR2520666
  
• [9] Bru, B., Bru, M.-F. and Chung, K. L. (2009). Borel and the St. Petersburg martingale. Electronic J. History Probab. Statist. 5. Available at www.jehps.net.
  Mathematical Reviews (MathSciNet): MR2520662
  
• [10] Cox, D. R. (2006). Principles of Statistical Inference. Cambridge Univ. Press, Cambridge.
  Mathematical Reviews (MathSciNet): MR2278763
  Zentralblatt MATH: 1102.62002
  
• [11] Dawid, A. P. (1984). Statistical theory: The prequential approach. J. Roy. Statist. Soc. Ser. A 147 278–292.
  Mathematical Reviews (MathSciNet): MR763811
  Digital Object Identifier: doi:10.2307/2981683
  JSTOR: links.jstor.org
  
• [12] Dawid, A. P., de Rooij, S., Shafer, G., Shen, A., Vereshchagin, N. and Vovk, V. (2011). Insuring against loss of evidence in game-theoretic probability. Statist. Probab. Lett. 81 157–162.
• [13] Dellacherie, C. and Meyer, P.-A. (1982). Probabilities and Potential B: Theory of Martingales. North-Holland, Amsterdam.
  Mathematical Reviews (MathSciNet): MR745449
  Zentralblatt MATH: 0494.60002
  
• [14] Dempster, A. P. (1969). Elements of Continuous Multivariate Analysis. Addison-Wesley, Reading, MA.
• [15] Edwards, W., Lindman, H. and Savage, L. J. (1963). Bayesian statistical inference for psychological research. Psychological Review 70 193–242.
  Mathematical Reviews (MathSciNet): MR1532349
  Digital Object Identifier: doi:10.2307/2312706
  
• [16] Fisher, R. A. (1925). Statistical Methods for Research Workers. Oliver and Boyd, Edinburgh.
• [17] Hipp, C. and Mattner, L. (2007). On the normal approximation to symmetric binomial distributions. Teor. Veroyatn. Primen. 52 610–617.
  Mathematical Reviews (MathSciNet): MR2743033
  
• [18] Itô, K. and Watanabe, S. (1965). Transformation of Markov processes by multiplicative functionals. Ann. l’Inst. Fourier 15 15–30.
  Mathematical Reviews (MathSciNet): MR184282
  
• [19] Johnson, G. and Helms, L. L. (1963). Class D supermartingales. Bull. Amer. Math. Soc. 69 59–62.
  Mathematical Reviews (MathSciNet): MR142148
  Zentralblatt MATH: 0133.40402
  Digital Object Identifier: doi:10.1090/S0002-9904-1963-10857-5
  Project Euclid: euclid.bams/1183525009
  
• [20] Kass, R. E. and Raftery, A. E. (1995). Bayes factors. J. Amer. Statist. Assoc. 90 773–795.
• [21] Lai, T. L. (2009). Martingales in sequential analysis and time series, 1945–1985. Electronic J. History Probab. Statist. 5. Available at www.jehps.net.
  Mathematical Reviews (MathSciNet): MR2520670
  
• [22] Laplace, P. S. (1774). Mémoire sur la probabilité des causes par les évènemens. Savants étranges 6 621–656. English translation (1986): Memoir on the probability of the causes of events. Statist. Sci. 1 364–378.
• [23] Lehmann, E. L. (2006). Nonparametrics: Statistical Methods Based on Ranks, revised 1st ed. Springer, New York.
  Mathematical Reviews (MathSciNet): MR2279708
  
• [24] Lévy, P. (1937). Théorie de l’addition des variables aléatoires. Gauthier-Villars, Paris.
• [25] Li, M. and Vitányi, P. (2008). An Introduction to Kolmogorov Complexity and Its Applications, 3rd ed. Springer, New York.
• [26] Locker, B. (2009). Doob at Lyon. Electronic J. History Probab. Statist. 5. Available at www.jehps.net.
  Mathematical Reviews (MathSciNet): MR2520667
  
• [27] Martin-Löf, P. (1966). Algorithmen und zufällige Folgen. Vier Vorträge von Per Martin-Löf (Stockholm) gehalten am Mathematischen Institut der Universität Erlangen-Nürnberg, Erlangen. This document, dated 16 April 1966, consists of notes taken by K. Jacobs and W. Müller from lectures by Martin-Löf at Erlangen on April 5, 6, 14, and 15. There are copies in several university libraries in Germany and the United States. Available at www.probabilityandfinance. com/misc/erlangen.pdf.
• [28] Martin-Löf, P. (1969). The literature on von Mises’ Kollektivs revisited. Theoria 35 12–37.
  Mathematical Reviews (MathSciNet): MR240841
  
• [29] Medvegyev, P. (2007). Stochastic Integration Theory. Oxford Univ. Press, Oxford.
  Mathematical Reviews (MathSciNet): MR2345169
  Zentralblatt MATH: 1153.60002
  
• [30] Meyer, P. A. (1966). Probability and Potentials. Blaisdell, Waltham, MA.
  Mathematical Reviews (MathSciNet): MR205288
  
• [31] Neyman, J. and Pearson, E. (1933). On the problem of the most efficient tests of statistical hypotheses. Philos. Trans. Roy. Soc. London Ser. A 231 289–337.
• [32] Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philos. Magazine 50 157–175.
• [33] R Development Core Team (2010). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna.
• [34] Schnorr, C.-P. (1971). Zufälligkeit und Wahrscheinlichkeit. Eine algorithmische Begründung der Wahrscheinlichkeitstheorie. Springer, Berlin.
• [35] Sellke, T., Bayarri, M. J. and Berger, J. (2001). Calibration of p-values for testing precise null hypotheses. Amer. Statist. 55 62–71.
  Mathematical Reviews (MathSciNet): MR1818723
  Zentralblatt MATH: 1182.62053
  Digital Object Identifier: doi:10.1198/000313001300339950
  JSTOR: links.jstor.org
  
• [36] Shafer, G. (2006). From Cournot’s principle to market efficiency. The Game-Theoretic Probability and Finance project, Working Paper 15. Available at probabilityandfinance.com.
• [37] Stigler, S. M. (1986). Laplace’s 1774 memoir on inverse probability. Statist. Sci. 1 359–363.
  Mathematical Reviews (MathSciNet): MR858515
  Digital Object Identifier: doi:10.1214/ss/1177013620
  Project Euclid: euclid.ss/1177013620
  
• [38] Todhunter, I. (1865). A History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace. Macmillan, London.
• [39] Ville, J. (1939). Etude critique de la notion de collectif. Gauthier-Villars, Paris.
• [40] Vovk, V. (1987). The law of the iterated logarithm for random Kolmogorov, or chaotic, sequences. Theory Probab. Appl. 32 413–425. Russian original: Закон повторного логарифма для случайных по Колмогорову, или хаотических, последовательностей. Теория вероятностей и ее применения 32 456–468.
  Mathematical Reviews (MathSciNet): MR914936
  
• [41] Vovk, V. (1993). A logic of probability, with application to the foundations of statistics (with discussion). J. Roy. Statist. Soc. Ser. B 55 317–351.
  Mathematical Reviews (MathSciNet): MR1224399
  JSTOR: links.jstor.org
  
• [42] Vovk, V., Gammerman, A. and Shafer, G. (2005). Algorithmic Learning in a Random World. Springer, New York.
  Mathematical Reviews (MathSciNet): MR2161220
  Zentralblatt MATH: 1105.68052
  
• [43] Wagenmakers, E.-J. (2007). A practical solution to the pervasive problems of p-values. Psychon. Bull. Rev. 14 779–804.