STATISTICAL SCIENCE Volume 35, Number 2 May 2020
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STATISTICAL SCIENCE Volume 35, Number 2 May 2020 Laplace’s Theories of Cognitive Illusions, Heuristics, and Biases ........................................................Joshua B. Miller and Andrew Gelman 159 Comment:LaplaceandCognitiveIllusions.........Daniel Kahneman and Maya Bar-Hillel 171 Comment:Illusions,ThenandNow............................................Glenn Shafer 173 Rejoinder: Laplace’s theories of cognitive illusions, heuristics and biases .....................................................Joshua B. Miller and Andrew Gelman 175 Fano’s Inequality for Random Variables .....................................Sébastien Gerchinovitz, Pierre Ménard and Gilles Stoltz 178 Equitability, Interval Estimation, and Statistical Power ..............Yakir A. Reshef, David N. Reshef, Pardis C. Sabeti and Michael Mitzenmacher 202 LGM Split Sampler: An Efficient MCMC Sampling Scheme for Latent Gaussian Models .............Óli Páll Geirsson, Birgir Hrafnkelsson, Daniel Simpson and Helgi Sigurdarson 218 Checking for Prior-Data Conflict Using Prior-to-Posterior Divergences .................... David J. Nott, Xueou Wang, Michael Evans and Berthold-Georg Englert 234 A Generalized Approach to Power Analysis for Local Average Treatment Effects...........................................................................Kirk Bansak 254 On the Probability That Two Random Integers Are Coprime . Jing Lei and Joseph B. Kadane 272 Comparative Study of Differentially Private Data Synthesis Methods .......................................................... Claire McKay Bowen and Fang Liu 280 AConversationwithGraceWahba..............Douglas Nychka, Ping Ma and Douglas Bates 308 A Conversation with Francisco J. Samaniego . George G. Roussas and Debasis Bhattacharya 321 Statistical Science [ISSN 0883-4237 (print); ISSN 2168-8745 (online)], Volume 35, Number 2, May 2020. Published quarterly by the Institute of Mathematical Statistics, 3163 Somerset Drive, Cleveland, OH 44122, 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, 9650 Rockville Pike—Suite L2310, Bethesda, MD 20814-3998, USA. Copyright © 2020 by the Institute of Mathematical Statistics Printed in the United States of America Statistical Science Volume 35, Number 2 (159–333) May 2020 Volume 35 Number 2 May 2020 Laplace’s Theories of Cognitive Illusions, Heuristics, and Biases Joshua B. Miller and Andrew Gelman Fano’s Inequality for Random Variables Sébastien Gerchinovitz, Pierre Ménard and Gilles Stoltz Equitability, Interval Estimation, and Statistical Power Yakir A. Reshef, David N. Reshef, Pardis C. Sabeti and Michael Mitzenmacher LGM Split Sampler: An Efficient MCMC Sampling Scheme for Latent Gaussian Models Óli Páll Geirsson, Birgir Hrafnkelsson, Daniel Simpson and Helgi Sigurdarson Checking for Prior-Data Conflict Using Prior-to-Posterior Divergences David J. Nott, Xueou Wang, Michael Evans and Berthold-Georg Englert A Generalized Approach to Power Analysis for Local Average Treatment Effects Kirk Bansak On the Probability That Two Random Integers Are Coprime Jing Lei and Joseph B. Kadane Comparative Study of Differentially Private Data Synthesis Methods Claire McKay Bowen and Fang Liu A Conversation with Grace Wahba Douglas Nychka, Ping Ma and Douglas Bates A Conversation with Francisco J. Samaniego George G. Roussas and Debasis Bhattacharya EDITOR Sonia Petrone Università Bocconi DEPUTY EDITOR Peter Green University of Bristol and University of Technology Sydney ASSOCIATE EDITORS Shankar Bhamidi Michael I. Jordan Glenn Shafer University of North Carolina University of California, Rutgers Business Peter Bühlmann Berkeley School–Newark and ETH Zürich Theo Kypraios New Brunswick Jiahua Chen University of Nottingham Royal Holloway College, University of British Columbia Ian McKeague University of London Rong Chen Columbia University Michael Stein Rutgers University Vladimir Minin University of Chicago Rainer Dahlhaus University of California, Irvine Jon Wellner University of Heidelberg Peter Müller University of Washington Robin Evans University of Texas Yihong Wu University of Oxford Luc Pronzato Yale University Stefano Favaro Université Nice Minge Xie Università di Torino Nancy Reid Rutgers University Peter Green University of Toronto Bin Yu University of Bristol and Jason Roy University of California, University of Technology Rutgers University Berkeley Sydney Chiara Sabatti Giacomo Zanella Susan Holmes Stanford University Università Bocconi Stanford University Richard Samworth Cun-Hui Zhang Tailen Hsing University of Cambridge Rutgers University University of Michigan Bodhisattva Sen Harrison Zhou Columbia University Yale University 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 2020, Vol. 35, No. 2, 159–170 https://doi.org/10.1214/19-STS696 © Institute of Mathematical Statistics, 2020 Laplace’s Theories of Cognitive Illusions, Heuristics and Biases Joshua B. Miller and Andrew Gelman Abstract. In his book from the early 1800s, Essai Philosophique sur les Probabilités, the mathematician Pierre-Simon de Laplace anticipated many ideas developed within the past 50 years in cognitive psychology and be- havioral economics, explaining human tendencies to deviate from norms of rationality in the presence of probability and uncertainty. A look at Laplace’s theories and reasoning is striking, both in how modern they seem, how much progress he made without the benefit of systematic experimentation, and the novelty of a few of his unexplored conjectures. We argue that this work points to these theories being more fundamental and less contingent on recent ex- perimental findings than we might have thought. REFERENCES EDWARDS, W. (1968). Conservatism in Human Information Process- ing. Wiley, New York. ASHRAF,N.,CAMERER,C.andLOEWENSTEIN, G. (2005). Adam ELSTER, J. (1989). Nuts and Bolts for the Social Sciences. Cambridge Smith, behavioral economist. J. Econ. Perspect. 19 131–145. Univ. Press, Cambridge. AYTON,P.andFISCHER, I. (2004). The hot hand fallacy and the EPLEY,N.andGILOVICH, T. (2006). The anchoring-and-adjustment gambler’s fallacy: Two faces of subjective randomness? Memory heuristic: Why the adjustments are insufficient. Psychol. Sci. 17 & Cognition 21 1369–1378. 311–318. BAR-HILLEL, M. (1980). 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