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STATISTICAL SCIENCE Volume 36, Number 3 August 2021 Khinchin’s 1929 Paper on Von Mises’ Frequency Theory of Probability . Lukas M. Verburgt 339 A Problem in Forensic Science Highlighting the Differences between the Bayes Factor and LikelihoodRatio...........................Danica M. Ommen and Christopher P. Saunders 344 A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach ..................................................................Axel Bücher and Chen Zhou 360 A Hybrid Scan Gibbs Sampler for Bayesian Models with Latent Variables ..........................Grant Backlund, James P. Hobert, Yeun Ji Jung and Kshitij Khare 379 Maximum Likelihood Multiple Imputation: Faster Imputations and Consistent Standard ErrorsWithoutPosteriorDraws...............Paul T. von Hippel and Jonathan W. Bartlett 400 RandomMatrixTheoryandItsApplications.............................Alan Julian Izenman 421 The GENIUS Approach to Robust Mendelian Randomization Inference .....................................Eric Tchetgen Tchetgen, BaoLuo Sun and Stefan Walter 443 AGeneralFrameworkfortheAnalysisofAdaptiveExperiments............Ian C. Marschner 465 Statistical Science [ISSN 0883-4237 (print); ISSN 2168-8745 (online)], Volume 36, Number 3, August 2021. Published quarterly by the Institute of Mathematical Statistics, 9760 Smith Road, Waite Hill, Ohio 44094, USA. Periodicals postage paid at Cleveland, Ohio and at additional mailing offices. POSTMASTER: Send address changes to Statistical Science, Institute of Mathematical Statistics, Dues and Subscriptions Office, PO Box 729, Middletown, Maryland 21769, USA. Copyright © 2021 by the Institute of Mathematical Statistics Printed in the United States of America Statistical Science Volume 36, Number 3 (339–492) August 2021 Volume 36 Number 3 August 2021 Khinchin’s 1929 Paper on Von Mises’ Frequency Theory of Probability Lukas M. Verburgt A Problem in Forensic Science Highlighting the Differences between the Bayes Factor and Likelihood Ratio Danica M. Ommen and Christopher P.Saunders A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach Axel Bücher and Chen Zhou A Hybrid Scan Gibbs Sampler for Bayesian Models with Latent Variables Grant Backlund, James P.Hobert, Yeun Ji Jung and Kshitij Khare Maximum Likelihood Multiple Imputation: Faster Imputations and Consistent Standard Errors Without Posterior Draws Paul T. von Hippel and Jonathan W. Bartlett Random Matrix Theory and Its Applications Alan Julian Izenman The GENIUS Approach to Robust Mendelian Randomization Inference Eric Tchetgen Tchetgen, BaoLuo Sun and Stefan Walter A General Framework for the Analysis of Adaptive Experiments Ian C. Marschner EDITOR Sonia Petrone Università Bocconi DEPUTY EDITOR Peter Green University of Bristol and University of Technology Sydney ASSOCIATE EDITORS Shankar Bhamidi Chris Holmes Chiara Sabatti University of North Carolina University of Oxford Stanford University Jay Breidt Susan Holmes Bodhisattva Sen Colorado State University Stanford University Columbia University Peter Bühlmann Tailen Hsing Glenn Shafer ETH Zürich University of Michigan Rutgers Business John Chambers Michael I. Jordan School–Newark and Stanford University University of California, New Brunswick Michael J. Daniels Berkeley Royal Holloway College, University of Florida Nicole Lazar University of London Philip Dawid Penn State University Jon Wellner University of Cambridge Ian McKeague University of Washington Robin Evans Columbia University Bin Yu University of Oxford Peter Müller University of California, Stefano Favaro University of Texas Berkeley Università di Torino Luc Pronzato Giacomo Zanella Alan Gelfand Université Nice Università Bocconi Duke University Nancy Reid Cun-Hui Zhang Peter Green University of Toronto Rutgers University University of Bristol and Jason Roy University of Technology Rutgers University Sydney MANAGING EDITOR Robert Keener University of Michigan PRODUCTION EDITOR Patrick Kelly EDITORIAL COORDINATOR Kristina Mattson PAST EXECUTIVE EDITORS Morris H. DeGroot, 1986–1988 Morris Eaton, 2001 Carl N. Morris, 1989–1991 George Casella, 2002–2004 Robert E. Kass, 1992–1994 Edward I. George, 2005–2007 Paul Switzer, 1995–1997 David Madigan, 2008–2010 Leon J. Gleser, 1998–2000 Jon A. Wellner, 2011–2013 Richard Tweedie, 2001 Peter Green, 2014–2016 Cun-Hui Zhang, 2017–2019 Statistical Science 2021, Vol. 36, No. 3, 339–343 https://doi.org/10.1214/20-STS798 © Institute of Mathematical Statistics, 2021 Khinchin’s 1929 Paper on Von Mises’ Frequency Theory of Probability Lukas M. Verburgt Abstract. In 1929, a few years prior to his colleague Kolmogorov’s Grund- begriffe, the leading Russian probabilist Khinchin published a paper in which he commented on the foundational ambitions of von Mises’ frequency theory of probability. This brief introduction provides background and context for the English translation of Khinchin’s historically revealing paper, published as an online supplement. Key words and phrases: Khinchin, Kolmogorov, von Mises, foundations of probability theory, frequency theory of probability, history of mathematics. REFERENCES KHINCHIN,A.YA. (1926). Ideas of intuitionism and the struggle for a subject matter in modern mathematics (Russian). Vestnik Kommu- BERNHARDT, H. (1984). Richard Von Mises und Sein Beitrag zur nisticheskoy Akademii 16 184–192. English translation in [Verburgt Grundlegung der Wahrscheinlichkeitsrechnung Im 20. Jahrhun- & Hoppe-Kondrikova, 2016]. dert. Habilitationsschrift, Berlin, Humboldt-Univ. KHINTCHINE,A.YA. (1927). Über das Gesetz der großen Zahlen. BINGHAM, N. H. (2001). Probability and statistics: Some thoughts at Math. Ann. 96 152–168. MR1512310 https://doi.org/10.1007/ the turn of the millennium. In Probability Theory (Roskilde, 1998) BF01209158 (V. F. Hendricks, S. A. Pedersen and K. F. Jorgensen, eds.). Syn- KHINCHIN,A.YA. (1929). The role and character of induction in these Lib. 297 15–49. Kluwer Academic, Dordrecht. MR1894707 mathematics (Russian). Vestnik Kommunisticheskoy Academii 1 5– CARNAP, R. (1934). Logische Syntax der Sprache. Springer, Vienna. 7. CHAUMONT,L.,MAZLIAK,L.andYOR, M. (2007). Some aspects of KHINCHIN,A.YA. (1933). Zur mathematischen Begründung der the probabilistic work. In Kolmogorov’s Heritage in Mathematics statistischen Mechanik. ZAMM Z. Angew. Math. Mech. 13 101– (E. Charpentier, A. Lesne and N. Nikolski, eds.) 41–66. Springer, 103. Berlin. MR2376738 https://doi.org/10.1007/978-3-540-36351-4_3 KHINCHIN,A.YA. (1952). The method of arbitrary functions and the CRAMÉR, H. (1962). A. I. Khinchin’s work in mathematical probabil- ity. Ann. Math. Stat. 33 1227–1237. MR0139512 https://doi.org/10. struggle against idealism in the theory of probability. (Russian). 1214/aoms/1177704355 Filosofskiye Sovremennoy Fiziki 522–538. HINCHIN A DOOB, J. L. (1996). The development of rigor in mathematical K ,A.Y . (1961). Mises’ frequentist theory and the mod- probability (1900–1950). Amer. Math. Monthly 103 586–595. ern ideas in the theory of probability (Russian). Voprosy Filosofii. MR1404084 https://doi.org/10.2307/2974673 Nauchno-tekhnicheskiy Zhurnal 15 (1), 92–102, 15 (2): 77–89. DÖRGE, K. (1930). Zu der von R. von Mises gegebenen Begründung KHINCHIN,A.YA. (2004 [1936–1944]). Mises’ frequentist theory der Wahrscheinlichkeitsrechnung. Erste Mitteilung: Theorie des and the modern ideas in the theory of probability. Translated by Glücksspiels. Math. Z. 32 232–258. MR1545164 https://doi.org/10. O. Sheynin, with footnotes by Reinhard Siegmund-Schultze. Sci. 1007/BF01194632 Context 17 319–422. MR2106024 GNEDENKO, B. V. (1961). Alexander Iacovlevich Khinchin. In Proc. KHINCHIN,A.YA. (1929 [2020]). Mises’ teachings on probabil- 4th Berkeley Sympos. Math. Statist. and Prob., Vol. II 1–15. (1 ity and the principles of statistical physics’. Translated from the plate). Univ. California Press, Berkeley, CA. MR0131956 original Russian by Laurent Mazliak, Lukas M. Verburgt and Olga HAUSDORFF, F. (2006). Gesammelte Werke. Band V. Astronomie, Op- Hoppe-Kondrikova. tik und Wahrscheinlichkeitstheorie. Springer, Berlin. MR2229144 LYUSTERNIK, L. A. (1967). The early years of the Moscow mathe- HOCHKIRCHEN, T. (1999). Die Axiomatisierung der Wahrschein- matics school. III. Russian Math. Surveys 22 55–91. lichkeitsrechnung und Ihre Kontexte. Von Hilberts sechstem Prob- MARTIN-LÖF, P. (1969). The literature on von Mises’ Kollektivs re- lem zu Kolmogoroffs Grundbegriffen. Studien zur Wissenschafts-, visited. Theoria 35 12–37. MR0240841 https://doi.org/10.1111/j. Sozial- und Bildungsgeschichte der Mathematik [Studies on the Sci- 1755-2567.1969.tb00357.x entific, Social and Educational History of Mathematics] 13.Van- PECHENKIN, A. (2014). Leonid Isaakovich Mandelstam: Research, denhoeck & Ruprecht, Göttingen. MR1738288 Teaching, Life. Springer, Cham. MR3235276 https://doi.org/10. KAMKE, E. (1932). Einführung in die Wahrscheinlichkeitstheorie. 1007/978-3-319-00572-0 Hirzel, Leipzig. MR0010917 PHILLIPS, E. R. (1978). Nicolai Nicolaevich Luzin and the Moscow KHINCHIN,A.YA. (1924). Über einen Satz der Wahrscheinlichkeit- school of the theory of functions. Historia Math. 5 275–305. srechnung. Fund. Math. 6 9–20. MR0500530 https://doi.org/10.1016/0315-0860(78)90114-3 Lukas M. Verburgt is Postdoctoral Researcher, Freudenthal Institute, History and Philosophy of Science, Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands (e-mail: [email protected]). SENETA, E. (1994). Russian probability and statistics before Kol- VERBURGT, L. M. (2021). Supplement
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