Bio


I am a mathematician and statistician working in probability, combinatorics, and group theory with a focus on applications to statistics and scientific computing. A specialty is rates of convergence of Markov chains. I am currently interested in trying to adapt the many mathematical developments to say something useful to practitioners in large real-world simulations.

Academic Appointments


Administrative Appointments


  • Visiting Professor, Université de Nice-Sophia Antipolis (2006 - 2007)
  • Fellow, Center for Advanced Study in the Behavioral Sciences (1999 - 2000)
  • Professor of Mathematics, Stanford University (1998 - Present)
  • Mary Sunseri Professor, Department of Statistics, Stanford University (1998 - Present)
  • David Duncan Professor, Department of Mathematics and ORIE, Cornell University (1996 - 1998)
  • George Vasmer Leverett Professor of Mathematics, Harvard University (1987 - 1997)
  • Professor of Statistics, Stanford University (1981 - 1987)
  • Visiting Professor, Department of Mathematics, Massachusetts Institute of Technology (1985 - 1986)
  • Visiting Professor, Department of Mathematics, Harvard University (1985 - 1986)
  • Visiting Professor, Department of Statistics, Harvard University (1981 - 1982)
  • Associate Professor of Statistics, Stanford University (1979 - 1980)
  • Research Staff Member, AT&T Bell Laboratories (1978 - 1979)
  • Assistant Professor of Statistics, Stanford University (1974 - 1979)

Honors & Awards


  • Honorary Degree, Athens University of Economics and Business (2009)
  • Honorary Degree, Queen Mary University of London (2006)
  • Van Wijngaarden Award, Centrum voor Wiskunde en Informatica (2006)
  • Honorary Degree, Uppsala University (2005)
  • Honorary Degree, Université Paul Sabatier (2003)
  • Honorary Degree, University of Chicago (2003)
  • Plenary Speaker, International Congress of Mathematicians (1998)
  • Fellow, American Statistical Association (1994)
  • Fellow, American Academy of Arts and Sciences (1989)
  • MacArthur Fellowship, MacArthur Foundation (1982-1987)
  • Rollo Davidson Prize, Cambridge University (1981)
  • Fellow, Institute of Mathematical Statistics (1981)

Professional Education


  • B.S., College of the City of New York, Mathematics (1971)
  • M.A., Harvard University, Mathematical Statistics (1972)
  • Ph.D., Harvard University, Mathematical Statistics (1974)

Current Research and Scholarly Interests


Many of my publications during the past three years have focused on rates of convergence of Markov chains to their stationary distributions. This is an important part of applied probability and scientific computing. I am particularly pleased by (a) results with Phillip Wood showing that most birth and death chains on {0,1,...} do not show a sharp cut-off; (b) results with Jason Fulman and Susan Holmes giving a careful analysis of casino shuffling machines; (c) results with Sourav Chatterjee making new contributions to a practical physics problem, Bose-Einstein condensation.

I think I opened up two new areas in the study of Markov chains: rates of convergence to quasi-stationarity and the study of "features''. For the first, a host of absorbing Markov chains appear in genetics, biology, and queuing. These have quasi-stationary distributions: given that the chain has not been absorbed by time T, where is it likely to be? We ask about quantitative versions, how large does T have to be to make the asymptotics useful? The many tools available for ergodic chains need to be completely revised. These papers make a start at revising the geometric theory (Poincare, Cheeger, Nash, log Sobolev). For the second area, "features", often researchers don't care about all aspects of a chain, but are only interested in a few features; then the rates of convergence can change. I proved such things for riffle shuffling but now see how to do things for other chains.

In addition to my work on Markov chains, I have completed a number of statistical projects. One of the main ones is for the statistical analysis of graph and network data. Working with Sourav Chatterjee, Svante Janson, and Susan Holmes we built a theory to allow analysis of familiar exponential models. These can have surprising properties: sometimes N parameters can be accurately estimated based on a sample of size one and sometimes a large amount of data can still lead to inconsistent estimators. This work opened up the connection between statistics and the emerging area of graph limit theory. In turn, that connection has led to a torrent of follow-up work, conferences, and a slew of real-world applications.

One key topic in my work has been generalizations of de Finetti's notion of exchangeability. The graph work above leans on the connections I made between graph limit theory and the Aldous-Hoover theorem. In a different direction, working with Sergio Bacallado and Susan Holmes, I managed to develop a practical theory of "almost exchangeability'' and apply it to some biological problems. I am busy following this up with some more theoretical work on de Finetti-style representation theorems for approximate exchangeable data.

A very different statistical development is represented by my work with Bob Griffiths developing bivariate distributions for data with binomial or multinomial models, and with Bailey, et al. which combines my group-theoretic methods for analysis of designed experiments with more classical approaches of Bailey and Nelder's "general balance''. It is surprising that these important problems haven't been seriously treated to date. Finally, work with my students Bhaswar Bhattacharya and Sumit Mukherjee on generalizations of the birthday problem to random graphs has direct application to Friedman-Rafsky two-sample tests.

2016-17 Courses


All Publications


  • The Mathematics of the Flip and Horseshoe Shuffles AMERICAN MATHEMATICAL MONTHLY Butler, S., Diaconis, P., Graham, R. 2016; 123 (6): 542-556
  • Central limit theorems for some set partition statistics ADVANCES IN APPLIED MATHEMATICS Chern, B., Diaconis, P., Kane, D. M., Rhoades, R. C. 2015; 70: 92-105
  • de Finetti Priors using Markov chain Monte Carlo computations STATISTICS AND COMPUTING Bacallado, S., Diaconis, P., Holmes, S. 2015; 25 (4): 797-808
  • An introduction to multivariate Krawtchouk polynomials and their applications JOURNAL OF STATISTICAL PLANNING AND INFERENCE Diaconis, P., Griffiths, R. 2014; 154: 39-53
  • Carries, Group Theory, and Additive Combinatorics AMERICAN MATHEMATICAL MONTHLY Diaconis, P., Shao, X., Soundararajan, K. 2014; 121 (8): 674-688
  • Unseparated pairs and fixed points in random permutations ADVANCES IN APPLIED MATHEMATICS Diaconis, P., Evans, S. N., Graham, R. 2014; 61: 102-124
  • Combinatorics of balanced carries ADVANCES IN APPLIED MATHEMATICS Diaconis, P., Fulman, J. 2014; 59: 8-25
  • Convolution powers of complex functions on Z MATHEMATISCHE NACHRICHTEN Diaconis, P., Saloff-Coste, L. 2014; 287 (10): 1106-1130
  • Hopf algebras and Markov chains: two examples and a theory JOURNAL OF ALGEBRAIC COMBINATORICS Diaconis, P., Pang, C. Y., Ram, A. 2014; 39 (3): 527-585
  • Fluctuations of the Bose-Einstein condensate JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL Chatterjee, S., Diaconis, P. 2014; 47 (8)
  • An Introduction to Multivariate Krawtchouck Polynomials and their Applications Journal of Statistical Planning and Inference Diaconis, P., Griffiths, R. 2014
  • ESTIMATING AND UNDERSTANDING EXPONENTIAL RANDOM GRAPH MODELS ANNALS OF STATISTICS Chatterjee, S., Diaconis, P. 2013; 41 (5): 2428-2461

    View details for DOI 10.1214/13-AOS1155

    View details for Web of Science ID 000327746100006

  • Some things we've learned (about Markov chain Monte Carlo) BERNOULLI Diaconis, P. 2013; 19 (4): 1294-1305

    View details for DOI 10.3150/12-BEJSP09

    View details for Web of Science ID 000324346200009

  • ANALYSIS OF CASINO SHELF SHUFFLING MACHINES ANNALS OF APPLIED PROBABILITY Diaconis, P., Fulman, J., Holmes, S. 2013; 23 (4): 1692-1720

    View details for DOI 10.1214/12-AAP884

    View details for Web of Science ID 000321678200014

  • Random doubly stochastic tridiagonal matrices RANDOM STRUCTURES & ALGORITHMS Diaconis, P., Wood, P. M. 2013; 42 (4): 403-437

    View details for DOI 10.1002/rsa.20452

    View details for Web of Science ID 000319070400001

  • Note on a partition limit theorem for rank and crank BULLETIN OF THE LONDON MATHEMATICAL SOCIETY Diaconis, P., Janson, S., Rhoades, R. C. 2013; 45: 551-553
  • Interval Graph Limits ANNALS OF COMBINATORICS Diaconis, P., Holmes, S., Janson, S. 2013; 17 (1): 27-52
  • Sampling from a Manifold Advances in Modern Statistical Theory and Applications: A Festschrift in honor of Morris L. Eaton Diaconis, P., Holmes, S., Shahashahani, M. edited by Jones, G., Shen, X. Institute of Mathematical Statistics. 2013: 102-125
  • Closed Expressions for Averages of Set Partition Statistics International Journal of Modern Math Chern, B., Diaconis, P., Chatterjee, S. 2013
  • Carries, Group Theory and Additive Combinatorics American Mathematical Monthly Diaconis, P., Shao, X., Soundararajan, K. 2013
  • Fluctuations of the Bose-Einstein Condensate Journal of Physics A: Mathematical and Theoretical Chatterjee, S., Diaconis, P. 2013; 47 (8)
  • Foulkes characters, Eulerian idempotents, and an amazing matrix JOURNAL OF ALGEBRAIC COMBINATORICS Diaconis, P., Fulman, J. 2012; 36 (3): 425-440
  • Gibbs/Metropolis algorithms on a convex polytope MATHEMATISCHE ZEITSCHRIFT Diaconis, P., Lebeau, G., Michel, L. 2012; 272 (1-2): 109-129
  • A PROBABILISTIC INTERPRETATION OF THE MACDONALD POLYNOMIALS ANNALS OF PROBABILITY Diaconis, P., Ram, A. 2012; 40 (5): 1861-1896

    View details for DOI 10.1214/11-AOP674

    View details for Web of Science ID 000311005600001

  • On Dirichlet eigenvectors for neutral two-dimensional Markov chains ELECTRONIC JOURNAL OF PROBABILITY Champagnat, N., Diaconis, P., Miclo, L. 2012; 17: 1-41
  • Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras ADVANCES IN MATHEMATICS Aguiar, M., Andre, C., Benedetti, C., Bergeron, N., Chen, Z., Diaconis, P., Hendrickson, A., Hsiao, S., Isaacs, I. M., Jedwab, A., Johnson, K., Karaali, G., Lauve, A., Le, T., Lewis, S., Li, H., Magaard, K., Marberg, E., Novelli, J., Pang, A., Saliola, F., Tevlin, L., Thibon, J., Thiem, N., Venkateswaran, V., Vinroot, C. R., Yan, N., Zabrocki, M. 2012; 229 (4): 2310-2337
  • EXCHANGEABLE PAIRS OF BERNOULLI RANDOM VARIABLES, KRAWTCHOUCK POLYNOMIALS, AND EHRENFEST URNS AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS Diaconis, P., Griffiths, R. 2012; 54 (1): 81-101
  • On the spectral analysis of second-order Markov chains Annales de la Faculté des Sciences de Toulouse, Mathematiques Diaconis, P., Miclo, L. 2012; 22: 573-621
  • Riffle Shuffles with Biased Cuts Formal Power Series and Algebraic Combinatorics Conference Assaf, S., Diaconis, P., Soundararajan, K. 2012
  • RANDOM GRAPHS WITH A GIVEN DEGREE SEQUENCE ANNALS OF APPLIED PROBABILITY Chatterjee, S., Diaconis, P., Sly, A. 2011; 21 (4): 1400-1435

    View details for DOI 10.1214/10-AAP728

    View details for Web of Science ID 000294220500006

  • The Mathematics of Mixing Things Up JOURNAL OF STATISTICAL PHYSICS Diaconis, P. 2011; 144 (3): 445-458
  • Geometric analysis for the metropolis algorithm on Lipschitz domains INVENTIONES MATHEMATICAE Diaconis, P., Lebeau, G., Michel, L. 2011; 185 (2): 239-281
  • A RULE OF THUMB FOR RIFFLE SHUFFLING ANNALS OF APPLIED PROBABILITY Assaf, S., Diaconis, P., Soundararajan, K. 2011; 21 (3): 843-875

    View details for DOI 10.1214/10-AAP701

    View details for Web of Science ID 000291736600002

  • On Barycentric Subdivision COMBINATORICS PROBABILITY & COMPUTING Diaconis, P., Miclo, L. 2011; 20 (2): 213-237
  • Magical Mathematics: The Mathematical Ideas that Animate Great Magic Tricks Diaconis, P., Graham, R. Princeton University Press. 2011
  • STOCHASTIC ALTERNATING PROJECTIONS ILLINOIS JOURNAL OF MATHEMATICS Diaconis, P., Khare, K., Saloff-Coste, L. 2010; 54 (3): 963-979
  • ON ADDING A LIST OF NUMBERS (AND OTHER ONE-DEPENDENT DETERMINANTAL PROCESSES) BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Borodin, A., Diaconis, P., Fulman, J. 2010; 47 (4): 639-670
  • Functions of random walks on hyperplane arrangements ADVANCES IN APPLIED MATHEMATICS Athanasiadis, C. A., Diaconis, P. 2010; 45 (3): 410-437
  • Threads Through Group Theory CHARACTER THEORY OF FINITE GROUPS Diaconis, P. 2010; 524: 33-47
  • Geometric Analysis for the Metropolis Algorithm on Lipschitz Domains Inventiones Mathematicae Diaconis, P., Lebeau, G., Michel, L. 2010; 185 (2): 239-281
  • Properties of Uniform Doubly Stochastic Matrices Annals of Applied Probability Diaconis, P., Chatterjee, S., Sly, A. 2010
  • Gibbs Sampling, Conjugate Priors and Coupling Sankhya Diaconis, P., Khare, K., Saloff-Coste, L. 2010; 72-A (1): 136-169
  • Carries, Shuffling, and an Amazing Matrix AMERICAN MATHEMATICAL MONTHLY Diaconis, P., Fulman, J. 2009; 116 (9): 788-803
  • On Times to Quasi-stationarity for Birth and Death Processes JOURNAL OF THEORETICAL PROBABILITY Diaconis, P., Miclo, L. 2009; 22 (3): 558-586
  • Carries, shuffling, and symmetric functions ADVANCES IN APPLIED MATHEMATICS Diaconis, P., Fulman, J. 2009; 43 (2): 176-196
  • Micro-local analysis for the Metropolis algorithm MATHEMATISCHE ZEITSCHRIFT Diaconis, P., Lebeau, G. 2009; 262 (2): 411-447
  • SUPERCHARACTER FORMULAS FOR PATTERN GROUPS TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Diaconis, P., Thiem, N. 2009; 361 (7): 3501-3533
  • A Sequential Importance Sampling Algorithm for Generating Random Graphs With Prescribed Degrees Journal of Internet Mathematics Diaconis, P., Blitzstein, J. 2009; 6 (4): 489-522
  • Book Review: Probabilistic Symmetries and Invariance Principles by Olav Kallenberg, Probability and its Applications Bulletin of the American Mathematical Society Diaconis, P. 2009
  • Threshold Graph Limits and Random Threshold Graphs Journal of Internet Mathematics Diaconis, P., Holmes, S., Janson, S. 2009; 5 (3): 267-320
  • Riffle shuffles of a deck with repeated cards 21st International Conference on Formal Power Series and Algebraic Combinatorics Diaconis, P., Assaf, S., Soundararajan, K. 2009: 89--102
  • FASTEST MIXING MARKOV CHAIN ON GRAPHS WITH SYMMETRIES SIAM JOURNAL ON OPTIMIZATION Boyd, S., Diaconis, P., Parrilo, P., Xiao, L. 2009; 20 (2): 792-819

    View details for DOI 10.1137/070689413

    View details for Web of Science ID 000268859300011

  • On characterizations of Metropolis type algorithms in continuous time ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS Diaconis, P., Miclo, L. 2009; 6: 199-238
  • THE MARKOV CHAIN MONTE CARLO REVOLUTION BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Diaconis, P. 2009; 46 (2): 179-205
  • HORSESHOES IN MULTIDIMENSIONAL SCALING AND LOCAL KERNEL METHODS ANNALS OF APPLIED STATISTICS Diaconis, P., Goel, S., Holmes, S. 2008; 2 (3): 777-807

    View details for DOI 10.1214/08-AOAS165

    View details for Web of Science ID 000261057900001

  • On fixed points of permutations JOURNAL OF ALGEBRAIC COMBINATORICS Diaconis, P., Fulman, J., Guralnick, R. 2008; 28 (1): 189-218
  • Gibbs sampling, exponential families and orthogonal polynomials STATISTICAL SCIENCE Diaconis, P., Khare, K., Saloff-Coste, L. 2008; 23 (2): 151-178

    View details for DOI 10.1214/07-STS252

    View details for Web of Science ID 000259275400001

  • Supercharacters and superclasses for algebra groups TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Diaconis, P., Isaacs, I. M. 2008; 360 (5): 2359-2392
  • Comment: Gibbs Sampling, Exponential Families and Orthogonal Polynomials Statistical Science Berti, P., Consonni, G., Pratelli, L., Rigo, P., Diaconis, P. 2008; 23 (2): 179-182
  • Projection Pursuit for Discrete Data Probability and Statistics: Essays in Honor of David A. Freedman Diaconis, P., Salzman, J. Institute of Mathematical Statistics. 2008: 265-288
  • Products of Universal Cycles A lifetime of puzzles: a collection of puzzles in honor of Martin Gardner Diaconis, P., Graham, R. L. edited by Demain, E., Demaine, M., Rodgers, T. AK Peters, Ltd.. 2008: 35-55
  • Graph Limits and Exchangeable Random Graphs Rendiconti di Matematica Diaconis, P., Janson, S. 2008; VII (28): 33-61
  • Comment Journal of the American Statistical Association Diaconis, P., Lehmann, E. 2008; 103 (481): 16
  • Comment: Gibbs Sampling, Exponential Families and Orthogonal Polynomials Statistical Science Diaconis, P., Jones, G. L., Johnson, A. A. 2008; 23 (2): 183-186
  • Threshold Graph Limits and Random Threshold Graphs. Internet mathematics Diaconis, P., Holmes, S., Janson, S. 2008; 5 (3): 267-320

    Abstract

    We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.

    View details for PubMedID 20811581

  • Rejoinder: Gibbs Sampling, Exponential Families and Orthogonal Polynomials Statistical Science Diaconis, P., Khare, K., Saloff-Coste, L. 2008; 23 (2): 196-200
  • Shuffling Cards, Adding Numbers, and Symmetric Functions PROCEEDINGS OF THE NINETEENTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS Diaconis, P. 2008: 560-560
  • Dynamical bias in the coin toss SIAM REVIEW Diaconis, P., Holmes, S., Montgomery, R. 2007; 49 (2): 211-235
  • The Solutions to Elmsley's Problem Math Horizons Diaconis, P., Graham, R. L. 2007; 14: 22-27
  • Hit and Run as a Unifying Device Journal de la Société Française de Statistique Diaconis, P., Graham, R. L. 2007; 148 (4): 5-28
  • The fastest mixing Markov process on a graph and a connection to a maximum variance unfolding problem SIAM REVIEW Sun, J., Boyd, S., Xiao, L., Diaconis, P. 2006; 48 (4): 681-699
  • Separation cut-offs for birth and death chains ANNALS OF APPLIED PROBABILITY Diaconis, P., Saloff-Coste, L. 2006; 16 (4): 2098-2122
  • Bayesian analysis for reversible Markov chains ANNALS OF STATISTICS Diaconis, P., Rolles, S. W. 2006; 34 (3): 1270-1292
  • Examples comparing importance sampling and the metropolis algorithm ILLINOIS JOURNAL OF MATHEMATICS Bassetti, F., Diaconis, P. 2006; 50 (1): 67-91
  • Markov bases for noncommutative Fourier analysis of ranked data JOURNAL OF SYMBOLIC COMPUTATION Diaconis, P., Eriksson, N. 2006; 41 (2): 182-195
  • Fastest mixing Markov chain on a path AMERICAN MATHEMATICAL MONTHLY Boyd, S., Diaconis, P., Sun, J., Xiao, L. 2006; 113 (1): 70-74
  • Mathematical Statistics Princeton Companion for Mathematics Diaconis, P. edited by Gowers, T. Princeton University Press. 2006
  • Sequential Monte Carlo methods for statistical analysis of tables JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Chen, Y. G., Diaconis, P., Holmes, S. R., Liu, J. S. 2005; 100 (469): 109-120
  • Analysis of a Bose-Einstein Markov chain ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES Diaconis, P. 2005; 41 (3): 409-418
  • Exchangeable Pairs and Poisson Approximation Probability Surveys Diaconis, P., Chatterjee, S., Meckes, E. 2005; 2 (1): 64-106
  • Symmetry Analysis of Reversible Markov Chains Journal of Internet Mathematics Diaconis, P., Boyd, S., Parrilo, P., Xiao, L. 2005; 2 (1): 31-71
  • What is...a Random Matrix Notices of the American Mathematical Society Diaconis, P. 2005; 52 (11): 1348-1349
  • Fastest mixing Markov chain on a graph SIAM REVIEW Boyd, S., Diaconis, P., Xiao, L. 2004; 46 (4): 667-689
  • A super-class walk on upper-triangular matrices JOURNAL OF ALGEBRA Arias-Castro, E., Diaconis, P., Stanley, R. 2004; 278 (2): 739-765
  • Random matrices, magic squares and matching polynomials ELECTRONIC JOURNAL OF COMBINATORICS Diaconis, P., Gamburd, A. 2004; 11 (2)
  • The Markov moment problem and de Finetti's theorem: Part II MATHEMATISCHE ZEITSCHRIFT Diaconis, P., Freedman, D. 2004; 247 (1): 201-212
  • The Markov moment problem and de Finetti's theorem: Part I MATHEMATISCHE ZEITSCHRIFT Diaconis, P., Freedman, D. 2004; 247 (1): 183-199
  • The Poisson-Dirichlet law is the unique invariant distribution for uniform split-merge transformations ANNALS OF PROBABILITY Diaconis, P., Mayer-Wolf, E., Zeitouni, O., Zerner, M. P. 2004; 32 (1B): 915-938
  • Uses of Exchangeable Pairs in Monte Carlo Markov Chains Stein's Method: Expository Lectures and Applications Diaconis, P., Stein, C., Holmes, S., Reinert, G. edited by Diaconis, P., Holmes, S. Institute of Mathematical Statistics. 2004: 1-26
  • On the Distribution of the Greatest Common Divisor A Festschrift for Herman Rubin Diaconis, P., Erdös, P. edited by Dasgupta, A. Institute of Mathematical Statistics. 2004: 126-137
  • Stein's Method for Markov Chains: First Examples Stein's Method: Expository Lectures and Applications Diaconis, P. edited by Diaconis, P., Holmes, S. Institute of Mathematical Statistics. 2004: 27-43
  • Numerical results for the metropolis algorithm EXPERIMENTAL MATHEMATICS Diaconis, P., Neuberger, J. W. 2004; 13 (2): 207-213
  • New tests of the correspondence between unitary eigenvalues and the zeros of Riemann's zeta function JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL Coram, M., Diaconis, P. 2003; 36 (12): 2883-2906
  • New Tests of the Correspondence Between Unitary Eigenvalues and the Zeros of Riemann's Zeta Functions Journal of Physics A: Mathematics and General Diaconis, P., Coram, M. 2003; 36 (12): 2883-2906
  • Brownian Motion and the Classical Groups Probability, Statistics and their applications: Papers in Honor of Rabii Bhattacharaya Diaconis, P., D'Aristotile, A., Newman, C. edited by Athreya, K., Majumdar, M., Puri, M., Waymire, E. Institute of Mathematical Statistics. 2003: 97-116
  • Randomn Walk on Groups: Characters and Geometry Groups St. Andrews, 2001 Diaconis, P. edited by Campbell, C. M., Roberson, E. F., Smith, G. C. Oxford: Cambridge University Press. 2003: 120-142
  • The Problem of Thinking Too Much Bulletin of the American Academy of Arts and Sciences Diaconis, P. 2003; LVI (3): 26-38
  • Mathematical Developments from the Analysis of Riffle-Shuffling Groups, Combinatorics and Geometry Diaconis, P. edited by Ivanov, A., Fuanou, A., Liebeck, M. World Scientific. 2003: 73-97
  • Patterns in eigenvalues: The 70th Josiah Willard Gibbs Lecture BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Diaconis, P. 2003; 40 (2): 155-178
  • G. H. Hardy and probability??? BULLETIN OF THE LONDON MATHEMATICAL SOCIETY Diaconis, P. 2002; 34: 385-402
  • The asymmetric one-dimensional constrained Ising model: Rigorous results JOURNAL OF STATISTICAL PHYSICS Aldous, D., Diaconis, P. 2002; 107 (5-6): 945-975
  • Toeplitz minors JOURNAL OF COMBINATORIAL THEORY SERIES A Bump, D., Diaconis, P. 2002; 97 (2): 252-271
  • A different construction of Gaussian fields from Markov chains: Dirichlet covariances ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES Diaconis, P., Evans, S. N. 2002; 38 (6): 863-878
  • Random Walk on Trees and Matchings Electronic Journal of Probability Diaconis, P., Holmes, S. 2002; 7: 1-17
  • Unitary correlations and the Fejer kernel - Dedicated to Harold Widom on his 70th birthday MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY Bump, D., Diaconis, P., Keller, J. B. 2002; 5 (2): 101-123
  • A geometric interpretation of the Metropolis-Hastings algorithm STATISTICAL SCIENCE Billera, L. J., Diaconis, P. 2001; 16 (4): 335-339
  • Combinatorics for the East model ADVANCES IN APPLIED MATHEMATICS Chung, F., Diaconis, P., Graham, R. 2001; 27 (1): 192-206
  • Chutes and ladders in Markov chains JOURNAL OF THEORETICAL PROBABILITY Diaconis, P., Durrett, R. 2001; 14 (3): 899-926
  • Statistical problems involving permutations with restricted positions STATE OF THE ART IN PROBABILITY AND STATISTICS: FESTSCHRIFT FOR WILLEM R VAN ZWET Diaconis, P., Graham, R., Holmes, S. P. 2001; 36: 195-222
  • Linear functionals of eigenvalues of random matrices TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Diaconis, P., Evans, S. N. 2001; 353 (7): 2615-2633
  • Analysis of a nonreversible Markov chain sampler ANNALS OF APPLIED PROBABILITY Diaconis, P., Holmes, S., Neal, R. M. 2000; 10 (3): 726-752
  • Immanants and finite point processes JOURNAL OF COMBINATORIAL THEORY SERIES A Diaconis, P., Evans, S. N. 2000; 91 (1-2): 305-321
  • Bounds for Kac's master equation COMMUNICATIONS IN MATHEMATICAL PHYSICS Diaconis, P., Saloff-Coste, L. 2000; 209 (3): 729-755
  • Analysis of systematic scan metropolis algorithms using Iwahori-Hecke algebra techniques MICHIGAN MATHEMATICAL JOURNAL Diaconis, P., Ram, A. 2000; 48: 157-190
  • A Bayesian Peek into Feller I Sankhya A Diaconis, P., Holmes, S. 2000; 64 (3): 820-841
  • Longest increasing subsequences: From patience sorting to the Baik-Deift-Johansson theorem BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Aldous, D., Diaconis, P. 1999; 36 (4): 413-432
  • Random walks and plane arrangements in three dimensions AMERICAN MATHEMATICAL MONTHLY Billera, L. J., Brown, K. S., Diaconis, P. 1999; 106 (6): 502-524
  • Iterated random functions SIAM REVIEW Diaconis, P., Freedman, D. 1999; 41 (1): 45-76
  • Matchings and phylogenetic trees PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Diaconis, P. W., Holmes, S. P. 1998; 95 (25): 14600-14602

    Abstract

    This paper presents a natural coordinate system for phylogenetic trees using a correspondence with the set of perfect matchings in the complete graph. This correspondence produces a distance between phylogenetic trees, and a way of enumerating all trees in a minimal step order. It is useful in randomized algorithms because it enables moves on the space of trees that make random optimization strategies "mix" quickly. It also promises a generalization to intermediary trees when data are not decisive as to their choice of tree, and a new way of constructing Bayesian priors on tree space.

    View details for Web of Science ID 000077436700005

    View details for PubMedID 9843935

  • A place for philosophy? The rise of modeling in statistical science QUARTERLY OF APPLIED MATHEMATICS Diaconis, P. 1998; 56 (4): 797-805
  • Consistency of Bayes estimates for nonparametric regression: normal theory BERNOULLI Diaconis, P. W., Freedman, D. 1998; 4 (4): 411-444
  • Walks on generating sets of groups INVENTIONES MATHEMATICAE Diaconis, P., Saloff-Coste, L. 1998; 134 (2): 251-299
  • Random walks and hyperplane arrangements ANNALS OF PROBABILITY Brown, K. S., Diaconis, P. 1998; 26 (4): 1813-1854
  • What do we know about the metropolis algorithm? JOURNAL OF COMPUTER AND SYSTEM SCIENCES Diaconis, P., Saloff-Coste, L. 1998; 57 (1): 20-36
  • Algebraic algorithms for sampling from conditional distributions ANNALS OF STATISTICS Diaconis, P., Sturmfels, B. 1998; 26 (1): 363-397
  • Random Walk and Hyperplane Arrangements Annals of Probability Diaconis, P., Brown, K. 1998; 26 (4): 1813-1854
  • From Shuffling Cards to Walking Around the Building. An Introduction to Markov Chain Theory Proc. Int. Congress, Berlin Diaconis, P. 1998: 187-204
  • Magic Routledge Encyclopedia of Philosophy Diaconis, P. edited by Craig, E. Routledge. 1998
  • Lattice Walks and Primary Decomposition Mathematical Essays in Honor of Gian-Carlo Rota Diaconis, P., Eisenbud, D., Sturmfels, B. edited by Sagan, B., Stanley, R. P. 1998: 173-194
  • The Graph of Generating Sets of an Abelian Group Colloquium Mathematicum Diaconis, P., Graham, R. L. 1998: 31-38
  • Are there still things to do in Bayesian statistics? PROBABILITY, DYNAMICS AND CAUSALITY Diaconis, P., Holmes, S. 1997: 5-18
  • Consistency of Bayes Estimates for Non-Parametric Regression: A Review Festschrift for Lucien LeCam Diaconis, P., Freedman, D. edited by Pollard, D., Torgersen, E., Yang, G. L. New York: Springer. 1997: 157-166
  • Walks on generating sets of Abelian groups PROBABILITY THEORY AND RELATED FIELDS Diaconis, P., SALOFFCOSTE, L. 1996; 105 (3): 393-421
  • Nash inequalities for finite Markov chains JOURNAL OF THEORETICAL PROBABILITY Diaconis, P., SALOFFCOSTE, L. 1996; 9 (2): 459-510
  • The cutoff phenomenon in finite Markov chains PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Diaconis, P. 1996; 93 (4): 1659-1664

    Abstract

    Natural mixing processes modeled by Markov chains often show a sharp cutoff in their convergence to long-time behavior. This paper presents problems where the cutoff can be proved (card shuffling, the Ehrenfests' urn). It shows that chains with polynomial growth (drunkard's walk) do not show cutoffs. The best general understanding of such cutoffs (high multiplicity of second eigenvalues due to symmetry) is explored. Examples are given where the symmetry is broken but the cutoff phenomenon persists.

    View details for Web of Science ID A1996TW69800057

    View details for PubMedID 11607633

  • A Non-Measurable Tail Set Statistics, Probability and Game Theory, Papers in Honor of David Blackwell Diaconis, P., Blackwell, D. edited by Ferguson, T. S., Shapley, L. S., MacQueen, J. B. Institute of Mathematical Statistics. 1996: 1-5
  • Random Walks on Finite Groups: A Survey of Analytic Techniques Probability Measures on Groups XI Diaconis, P., Saloff-Coste, L. edited by Heyer, H. World Scientific Singapore. 1996: 44-75
  • Some New Tools for Dirichlet Priors, Proceedings of the Fifth Valencia International Meeting Bayesian Statistics 5 Diaconis, P. edited by Bernardo, J., Berger, J., Dawid, A., Smith, F. Oxford University Press. 1996: 97-106
  • Logarithmic Sobolev Inequalities for Finite Markov Chains Annals of Applied Probability Diaconis, P., Saloff-Coste, L. 1996; 6: 695-750
  • Metrics on Compositions and Coincidences Among Renewal Sequences Random Discrete Structures Diaconis, P., Holmes, S., Janson, S., Lalley, S. P., Pemantle, R. edited by Aldous, D., Pemantle, R. New York: Springer Verlag. 1996: 81-102
  • Primitive partition identities COMBINATORICS, PAUL ERDOS IS EIGHTY, VOL. 2 Diaconis, P., GRAHAM, R. L., Sturmfels, B. 1996; 2: 173-192
  • HAMMERSLEYS INTERACTING PARTICLE PROCESS AND LONGEST INCREASING SUBSEQUENCES PROBABILITY THEORY AND RELATED FIELDS Aldous, D., Diaconis, P. 1995; 103 (2): 199-213
  • What Do We Know About the Metropolis Algorithm? Proceedings of the 27th Symposium on Theory of Computing Diaconis, P., Saloff-Coste, L. 1995: 112-129
  • RIFFLE SHUFFLES, CYCLES, AND DESCENTS COMBINATORICA Diaconis, P., McGrath, M., Pitman, J. 1995; 15 (1): 11-29
  • An Application of Harnack Inequalities to Random Walk on Nilpotent Quotients Journal Fourier Analysis and Applications Diaconis, P., Saloff-Coste, L. 1995: 189-207
  • NonParametric Binary Regression with Random Covariates Probability and Mathematical Statistics Diaconis, P., Freedman, D. 1995; 15: 243-273
  • GRAY CODES FOR RANDOMIZATION PROCEDURES STATISTICS AND COMPUTING Diaconis, P., Holmes, S. 1994; 4 (4): 287-302
  • ON THE EIGENVALUES OF RANDOM MATRICES JOURNAL OF APPLIED PROBABILITY Diaconis, P., Shahshahani, M. 1994; 31A: 49-62
  • Three Examples of the Markov Chain Monte Carlo Method Discrete Probability and Algorithms Diaconis, P., Holmes, S. edited by Aldous, D., Saloff-Coste, L., Spencer, J., Steele, J. M. New York: Springer-Verlag. 1994: 43-56
  • MODERATE GROWTH AND RANDOM-WALK ON FINITE-GROUPS GEOMETRIC AND FUNCTIONAL ANALYSIS Diaconis, P., SALOFFCOSTE, L. 1994; 4 (1): 1-36
  • Rectangular Arrays With Fixed Margins Discrete Probability and Algorithms Diaconis, P., Gangolli, A. edited by Aldous, D., Saloff-Coste, L., Spencer, J., Steele, J. M. New York: Springer-Verlag. 1994: 15-42
  • SPECTRAL-ANALYSIS FOR DISCRETE LONGITUDINAL DATA ADVANCES IN MATHEMATICS Beckett, L., Diaconis, P. 1994; 103 (1): 107-128
  • NONPARAMETRIC BINARY REGRESSION - A BAYESIAN-APPROACH ANNALS OF STATISTICS Diaconis, P., Freedman, D. A. 1993; 21 (4): 2108-2137
  • COMPARISON TECHNIQUES FOR RANDOM-WALK ON FINITE-GROUPS ANNALS OF PROBABILITY Diaconis, P., SALOFFCOSTE, L. 1993; 21 (4): 2131-2156
  • Comparison Theorems for Reversible Markov Chains Annals of Applied Probability Diaconis, P., Saloff-Coste, L. 1993; 3 (3): 696-730
  • Non-Parametric Binary Bayesian Regression: A Bayesian Approach Annals of Statistics Diaconis, P., Freedman, D. 1993; 21: 2018-2137
  • DISCUSSION ON THE MEETING ON THE GIBBS SAMPLER AND OTHER MARKOV CHAIN-MONTE CARLO METHODS JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY Clifford, P., Jennison, C., Wakefield, J., Phillips, D., Frigessi, A., Gray, A. J., Lawson, A., Forster, J., RAMGOPAL, P., Arslan, O., Constable, P. D., Kent, J. T., Wolff, R. C., Harding, E. F., Middleton, R., Diggle, P. J., Aykroyd, R. G., Berzuini, C., Brewer, M., Aitken, C., Celeux, G., Diebolt, J., Critchley, F., Diaconis, P., Rosenthal, J. S., Diebolt, J., Robert, C. P., Gelfand, A. E., Lee, T. M., Gelman, A., Rubin, D. B., Geman, D., Geweke, J., Geyer, C. J., Gigli, A., Givens, G. H., Goodall, C., JONALASINIO, G. D., Grieve, A. P., Han, X. L., Kolassa, J. E., Tanner, M. A., Kooperberg, C., Lewis, S. M., Lin, S., Thompson, E. A., Litton, C. D., Buck, C. E., Liu, C. H., Liu, J., Mardia, K. V., Marriott, J. M., Moller, J., Raftery, A. E., Shephard, N., Sinha, D., SOKAL, A. D., Titterington, D. M., Wilson, J. D., York, J., Madigan, D., Smith, A. F., Roberts, G. O., Besag, J., Green, P. J., Gilks, W. R., Clayton, D. G., Spiegelhalter, D. J. 1993; 55 (1): 53-102
  • Foreward Probability Models and Statistical Analyses For Ranking Data Diaconis, P. edited by Fligner, M., Verducci, J. New York: Springer. 1993: xvii-xxiii
  • Efficient Computation of Isotypic Projections for the Symmetric Group DIMACS: Series in Discrete Mathematics and Theoretical Computer Science Diaconis, P., Rockmore, D. edited by Finkelstein, L., Kantor, W. Center for Discrete Mathematics and Theoretical Computer Science. 1993: 87-104
  • UNIVERSAL CYCLES FOR COMBINATORIAL STRUCTURES DISCRETE MATHEMATICS Chung, F., Diaconis, P., Graham, R. 1992; 110 (1-3): 43-59
  • BINOMIAL COEFFICIENT CODES OVER GF(2) DISCRETE MATHEMATICS Diaconis, P., Graham, R. 1992; 106: 181-188
  • AN AFFINE WALK ON THE HYPERCUBE JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Diaconis, P., Graham, R. 1992; 41 (1-2): 215-235
  • Analysis of Top to Random Shuffles Combinatorics, Probability and Computing Diaconis, P., Fill, J., Pitman, J. 1992; 1: 135-155
  • Non Parametric Binary Bayesian Regression Festschrift for Raj Bahaduhr Diaconis, P., Freedman, D. Indian Statistical Institute. 1992
  • Eigen-Analysis for Some Examples of the Metropolis Algorithm Contemporary Mathematics Diaconis, P., Hanlon, P. 1992; 138: 99-117
  • Trailing the Dovetail Shuffle to its Lair Annals of Applied Probablity Diaconis, P., Bayer, D. 1992; 2 (2): 294-313
  • Sufficiency as Statistical Symmetry Proceedings of the 100th Anniversary Americal Mathematical Society Diaconis, P. edited by Browder, F. Providence: American Mathematics Society. 1992: 15-26
  • Finite de Finetti Theorems in Linear Modules and Multivariate Analysis Scandinavian Journal of Statistics Diaconis, P., Eaton, M. L., Lauritzan, S. 1992; 19: 298-315
  • A Growth Model, A Game, An Algebra, Lagrange Inversion and Characteristic Classes Recondita Mathematics Diaconis, P., Fulton, W. 1991; 49: 95-119
  • Closed Form Summation for Classical Distributions: Variations on a Theme of Demoivre Statistical Science Diaconis, P., Zabell, S. 1991; 61 (3): 284-302
  • Geometric Bounds for Eigenvalues of Markov Chains Annals of Applied Probability Diaconis, P., Stroock, D. 1991; 1 (1): 36-61
  • STRONG STATIONARY TIMES VIA A NEW FORM OF DUALITY ANNALS OF PROBABILITY Diaconis, P., Fill, J. A. 1990; 18 (4): 1483-1522
  • ON THE UNIFORM CONSISTENCY OF BAYES ESTIMATES FOR MULTINOMIAL PROBABILITIES ANNALS OF STATISTICS Diaconis, P., Freedman, D. 1990; 18 (3): 1317-1327
  • Finite Fourier Methods: Access to Tols Probabalistic combinatorics, Proceedings of Symposia in Applied Mathematics Diaconis, P. 1990: 171-194
  • CAUCHYS EQUATION AND DEFINETTIS THEOREM SCANDINAVIAN JOURNAL OF STATISTICS Diaconis, P., Freedman, D. A. 1990; 17 (3): 235-250
  • Applications of Groups Representations to Statistical Problems Proceedings International Congress of Mathematician, Kyoto Diaconis, P. 1990: 1037-1048
  • Asymptotic Analysis of a Random Walk on a Hypercube with Many Dimensions Random Structures and Algorithms Diaconis, P., Graham, R. L., Morrison, J. A. 1990; 1: 51-72
  • Efficient Computation of the Fourier Transform on Finite Groups Journal of the American Mathematical Society Diaconis, P., Rockmore, D. 1990; 3 (2): 297-332
  • Patterned Matrices Matrix Theory and Applications: Proceedings of Symposia in Applied Mathematics, American Mathematical Society Diaconis, P. 1990: 37-58
  • Bounds for Tail Probabilities of Weighted Sums of Independent Gamma Random Variables Topics in Statistical Dependence Diaconis, P., Perlman, M. edited by Block, H. W., Sampson, A. R., Savits, T. H. Hayward, CA: Institute of Mathematical Statistics. 1990: 147-166
  • Examples for the Theory of Strong Stationary Duality with Countable State Spaces Probability in the Engineering and Informational Sciences Diaconis, P., Fill, J. 1990; 4: 157-180
  • Cauchy's Equation and de Finetti's Theorem Journal of Statistics Diaconis, P., Freedman, D. 1990; 17 (3): 235-250
  • METHODS FOR STUDYING COINCIDENCES JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Diaconis, P., Mosteller, F. 1989; 84 (408): 853-861
  • THE 1987 WALD MEMORIAL LECTURES - A GENERALIZATION OF SPECTRAL-ANALYSIS WITH APPLICATION TO RANKED DATA ANNALS OF STATISTICS Diaconis, P. 1989; 17 (3): 949-979
  • FAIR DICE AMERICAN MATHEMATICAL MONTHLY Diaconis, P., Keller, J. B. 1989; 96 (4): 337-339
  • Bounds for Tail Probabilities of Weighted Sums of Independent Gamma Random Variables Symposium on Dependence in Statistics and Probability Diaconis, P. 1989: 147-166
  • ON MERGING OF PROBABILITIES SANKHYA-THE INDIAN JOURNAL OF STATISTICS SERIES A DARISTOTILE, A., Diaconis, P., Freedman, D. 1988; 50: 363-380
  • HONEST BERNOULLI EXCURSIONS JOURNAL OF APPLIED PROBABILITY Smith, L., Diaconis, P. 1988; 25 (3): 464-477
  • Application of the Method of Moments in Probability and Statistics Moments in Mathematics Proceedings of Symposia in Applied Mathematics, American Mathematical Society Diaconis, P. 1988: 125-142
  • Conditional Limit Theorems for Exponential Families with Uniform Asymptotic Estimates and Applications to de Finetti's Theorem Theoretical Probability Diaconis, P., Freedman, D. 1988; 1: 381-410
  • Recent Progress in de Finetti's Notions of Exchangeability Bayesian Statistics 3: Proceedings of the Third Valencia International Meeting Diaconis, P., Bernardo, J., et al 1988: 111-125
  • Bayesian Numerical Analysis Statistical Decision Theory and Related Topics IV Diaconis, P. edited by Berger, J., Gupta, S. New York: Springer-Verlag. 1988: 163-175
  • INEQUALITIES FOR LINEAR-COMBINATIONS OF GAMMA-RANDOM VARIABLES CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE Bock, M. E., Diaconis, P., Huffer, F. W., Perlman, M. D. 1987; 15 (4): 387-395
  • WHAT IS AN ANALYSIS OF VARIANCE - DISCUSSION ANNALS OF STATISTICS Diaconis, P. 1987; 15 (3): 917-921
  • RANDOM-WALKS ARISING IN RANDOM NUMBER GENERATION ANNALS OF PROBABILITY Chung, F. R., Diaconis, P., GRAHAM, R. L. 1987; 15 (3): 1148-1165
  • STRONG UNIFORM TIMES AND FINITE RANDOM-WALKS ADVANCES IN APPLIED MATHEMATICS Aldous, D., Diaconis, P. 1987; 8 (1): 69-97
  • TIME TO REACH STATIONARITY IN THE BERNOULLI LAPLACE DIFFUSION-MODEL SIAM JOURNAL ON MATHEMATICAL ANALYSIS Diaconis, P., Shahshahani, M. 1987; 18 (1): 208-218
  • Probabilistic-Geometric Theorems Arising from the Analysis of Contingency Tables Contributions to the Theory and Application of Statistics, A Volume in Honor of Herbert Solomon Diaconis, P., Efron, B. Academic Press. 1987: 103-125
  • Fred Mosteller as a Mathematical Statistician A Statistical Model Diaconis, P., Lehmann, E. edited by Fienberg, S., Hoaglin, D., Kruskal, W., Tanur, J. New York: Springer-Verlag. 1987: 59-80
  • The Subgroup Algorithm for Generating Uniform Random Variables Probability in the Engineering and Informational Sciences Diaconis, P., Shahshahani, M. 1987; 1: 15-32
  • Projection Pursuit for Discrete Data Scandinavian Journal of Statistics Diaconis, P. 1987
  • A DOZEN DE FINETTI-STYLE RESULTS IN SEARCH OF A THEORY ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES Diaconis, P., Freedman, D. 1987; 23: 397-423
  • ON SQUARE ROOTS OF THE UNIFORM-DISTRIBUTION ON COMPACT-GROUPS PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Diaconis, P., Shahshahani, M. 1986; 98 (2): 341-348
  • SHUFFLING CARDS AND STOPPING-TIMES AMERICAN MATHEMATICAL MONTHLY Aldous, D., Diaconis, P. 1986; 93 (5): 333-348
  • ON THE CONSISTENCY OF BAYES ESTIMATES - REJOINDER ANNALS OF STATISTICS Diaconis, P., Freedman, D. 1986; 14 (1): 63-67
  • ON THE CONSISTENCY OF BAYES ESTIMATES ANNALS OF STATISTICS Diaconis, P., Freedman, D. 1986; 14 (1): 1-26
  • ON INCONSISTENT BAYES ESTIMATES OF LOCATION ANNALS OF STATISTICS Diaconis, P., Freedman, D. 1986; 14 (1): 68-87
  • AN ELEMENTARY PROOF OF STIRLING FORMULA AMERICAN MATHEMATICAL MONTHLY Diaconis, P., Freedman, D. 1986; 93 (2): 123-125
  • A Subjective Guide to Objective Chance Statistical Science Diaconis, P., Engel, E. 1986; 1: 171-174
  • Products of Random Matrices as They Arise in the Study of Random Walks on Groups Contemporary Mathematics Diaconis, P., Shahshahani, M. 1986; 50: 183-195
  • Products of Random Matrices and Computer Image Generation Contemporary Mathematics Diaconis, P., Shahshahani, M. 1986; 50: 173-182
  • Applications of Nonommutative Fourier Analysis to Probability Problems Ecolé d' Été de Probabilites de St. Flours, XV-XVII, Springer Lecture Notes in Mathematics Diaconis, P., et al Berlin: Springer-Verlag. 1986: 51-100
  • THE RADON-TRANSFORM ON Z2K PACIFIC JOURNAL OF MATHEMATICS Diaconis, P., GRAHAM, R. L. 1985; 118 (2): 323-345
  • Bayesian Statistics as Honest Work Proceedings of the Berkeley Conference in Honor of Jerzey Neyman and Jack Kiefer Diaconis, P. edited by LeCam, L., Olshen, R. 1985: 53-64
  • Some Alternatives to Bayes' Rule Information and Group Decision Making, Proceedings of the Second University of California, Irvine Conference on Political Economy Diaconis, P., Zabell, S. edited by Grofman, B., Owen, G. 1985: 25-38
  • Theories of Data Analysis: From Magical Thinking Through Classical Statistics Exploring Data Tables, Trends and Shapes Diaconis, P. edited by Hoaglin, D., Mosteller, F., Tukey, J. New York: Wiley. 1985: 1-36
  • Quantifying Prior Opinion Bayesian Statistics 2. Proceedings of the 2nd Valencia International Meeting Diaconis, P., Ylvisaker, D. edited by Bernardo, J. M., Degroot, M. H., Lindley, D. V., Smith, A. F. 1985: 133-156
  • TESTING FOR INDEPENDENCE IN A 2-WAY TABLE - NEW INTERPRETATIONS OF THE CHI-SQUARE STATISTIC ANNALS OF STATISTICS Diaconis, P., Efron, B. 1985; 13 (3): 845-874
  • TESTING FOR INDEPENDENCE IN A 2-WAY TABLE - NEW INTERPRETATIONS OF THE CHI-SQUARE STATISTIC - REJOINDER ANNALS OF STATISTICS Diaconis, P., Efron, B. 1985; 13 (3): 905-913
  • PROJECTION PURSUIT - DISCUSSION ANNALS OF STATISTICS Diaconis, P. 1985; 13 (2): 494-496
  • ON NONLINEAR FUNCTIONS OF LINEAR-COMBINATIONS SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING Diaconis, P., Shahshahani, M. 1984; 5 (1): 175-191
  • ASYMPTOTICS OF GRAPHICAL PROJECTION PURSUIT ANNALS OF STATISTICS Diaconis, P., Freedman, D. 1984; 12 (3): 793-815
  • The Mathematics of Perfect Shuffles Advances in Applied Mathematics Diaconis, P., Graham, R. L., Kantor, W. M. 1983; 4 (2): 175-196
  • M and N plots Recent Advances in Statistics Diaconis, P., Friedman, J. H. edited by Rizvi, H., Rustagi, J., Siegmund, D. New York: Academic Press. 1983: 425-447
  • Frequency Properties of Bayes Rules Scientific Inference, Data Analysis, and Robustness Diaconis, P., Freedman, D. edited by Box, G., Leonard, T., Wu, C. F. New York: Academic Press. 1983: 105-115
  • COMPUTER-INTENSIVE METHODS IN STATISTICS SCIENTIFIC AMERICAN Diaconis, P., Efron, B. 1983; 248 (5): 116-?
  • ON INCONSISTENT BAYES ESTIMATES IN THE DISCRETE CASE ANNALS OF STATISTICS Freedman, D., Diaconis, P. 1983; 11 (4): 1109-1118
  • ON THE MAXIMUM DIFFERENCE BETWEEN THE EMPIRICAL AND EXPECTED HISTOGRAMS FOR SUMS PACIFIC JOURNAL OF MATHEMATICS Diaconis, P., Freedman, D. 1982; 100 (2): 287-327
  • Bayes Rules for Location Problems Statistical Decision Theory and Related Topics III Diaconis, P., Freedman, D. edited by Gupta, S., Berger, J. 1982: 315-327
  • ON THE DIFFERENCE BETWEEN THE EMPIRICAL HISTOGRAM AND THE NORMAL CURVE, FOR SUMS .2. PACIFIC JOURNAL OF MATHEMATICS Diaconis, P., Freedman, D. 1982; 100 (2): 359-371
  • VARIABLES ON SCATTERPLOTS LOOK MORE HIGHLY CORRELATED WHEN THE SCALES ARE INCREASED SCIENCE Cleveland, W. S., Diaconis, P., McGill, R. 1982; 216 (4550): 1138-1141

    Abstract

    Judged association between two variables represented on scatterplots increased when the scales on the horizontal and vertical axes were simultaneously increased so that the size of the point cloud within the frame of the plot decreased. Judged association was very different from the correlation coefficient, r, which is the most widely used measure of association.

    View details for Web of Science ID A1982NR10700041

    View details for PubMedID 17808503

  • UPDATING SUBJECTIVE-PROBABILITY JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Diaconis, P., Zabell, S. L. 1982; 77 (380): 822-830
  • DE FINETTIS THEOREM FOR SYMMETRIC LOCATION FAMILIES ANNALS OF STATISTICS Freedman, D., Diaconis, P. 1982; 10 (1): 184-189
  • ON THE MODE OF AN EMPIRICAL HISTOGRAM FOR SUMS PACIFIC JOURNAL OF MATHEMATICS Diaconis, P., Freedman, D. 1982; 100 (2): 373-385
  • ON INCONSISTENT M-ESTIMATORS ANNALS OF STATISTICS Freedman, D. A., Diaconis, P. 1982; 10 (2): 454-461
  • ON THE STATISTICS OF VISION - THE JULESZ CONJECTURE JOURNAL OF MATHEMATICAL PSYCHOLOGY Diaconis, P., Freedman, D. 1981; 24 (2): 112-138
  • Magical Thinking in the Analysis of Scientific Data Annals of the New York Academy of Science Diaconis, P. 1981; 364: 236-244
  • Partial Exchangeability and Sufficiency Proceedings of the Indian Statistical Institute Golden Jubilee International Conference on Statistics: Applications and New Directions Diaconis, P., Freedman, D. edited by Ghosh, J. K., Roy, J. 1981: 205-236
  • On the Permanents of Complements of the Direct Sum of Identity Matrices Advances in Applied Mathematics Diaconis, P., Chung, F., Graham, R. L., Mallows, C. L. 1981; 2: 121-137
  • How Fast is the Fastest Fourier Transform Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface Diaconis, P. edited by Eddy, W. F. 1981
  • ON THE HISTOGRAM AS A DENSITY ESTIMATOR - L2 THEORY ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE Freedman, D., Diaconis, P. 1981; 57 (4): 453-476
  • THE ANALYSIS OF SEQUENTIAL EXPERIMENTS WITH FEEDBACK TO SUBJECTS ANNALS OF STATISTICS Diaconis, P., Graham, R. 1981; 9 (1): 3-23
  • THE PERSISTENCE OF COGNITIVE ILLUSIONS BEHAVIORAL AND BRAIN SCIENCES Diaconis, P., Freedman, D. 1981; 4 (3): 333-334
  • GENERATING A RANDOM PERMUTATION WITH RANDOM TRANSPOSITIONS ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE Diaconis, P., Shahshahani, M. 1981; 57 (2): 159-179
  • ON THE MAXIMUM DEVIATION BETWEEN THE HISTOGRAM AND THE UNDERLYING DENSITY ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE Freedman, D., Diaconis, P. 1981; 58 (2): 139-167
  • FINITE EXCHANGEABLE SEQUENCES ANNALS OF PROBABILITY Diaconis, P., Freedman, D. 1980; 8 (4): 745-764
  • Average Running Time of the Fast Fourier Transform Journal of Algorithms Diaconis, P. 1980; 1 (2): 187-208
  • DE FINETTI THEOREM FOR MARKOV-CHAINS ANNALS OF PROBABILITY Diaconis, P., Freedman, D. 1980; 8 (1): 115-130
  • de Finetti's Generalizations of Exchangeability Studies in Inductive Logic and Probability Diaconis, P. edited by Jeffrey, R. 1980
  • ROUNDING PERCENTAGES JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION Diaconis, P., Freedman, D. 1979; 74 (366): 359-364
  • CONJUGATE PRIORS FOR EXPONENTIAL FAMILIES ANNALS OF STATISTICS Diaconis, P., YLVISAKER, D. 1979; 7 (2): 269-281
  • SOME TAUBERIAN THEOREMS RELATED TO COIN TOSSING ANNALS OF PROBABILITY Diaconis, P., Stein, C. 1978; 6 (3): 483-490
  • STATISTICAL PROBLEMS IN ESP RESEARCH SCIENCE Diaconis, P. 1978; 201 (4351): 131-136

    Abstract

    In search of repeatable ESP experiments, modern investigators are using more complex targets, richer and freer responses, feedback, and more naturalistic conditions. This makes tractable statistical models less applicable. Moreover, controls often are so loose that no valid statistical analysis is possible. Some common problems are multiple end points, subject cheating, and unconscious sensory cueing. Unfortunately, such problems are hard to recognize from published records of the experiments in which they occur; rather, these problems are often uncovered by reports of independent skilled observers who were present during the experiment. This suggests that magicians and psychologists be regularly used as observers. New statistical ideas have been developed for some of the new experiments. For example, many modern ESP studies provide subjects with feedback--partial information about previous guesses--to reward the subjects for correct guesses in hope of inducing ESP learning. Some feedback experiments can be analyzed with the use of skill-scoring, a statistical procedure that depends on the information available and the way the guessing subject uses this information.

    View details for Web of Science ID A1978FE79500005

    View details for PubMedID 663642

  • 2ND-ORDER TERMS FOR VARIANCES AND COVARIANCES OF NUMBER OF PRIME FACTORS - INCLUDING SQUARE FREE CASE JOURNAL OF NUMBER THEORY Diaconis, P., Mosteller, F., Onishi, H. 1977; 9 (2): 187-202
  • SPEARMANS FOOTRULE AS A MEASURE OF DISARRAY JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY Diaconis, P., GRAHAM, R. L. 1977; 39 (2): 262-268
  • FINITE FORMS OF DE FINETTS THEOREM ON EXCHANGEABILITY SYNTHESE Diaconis, P. 1977; 36 (2): 271-281
  • DISTRIBUTION OF LEADING DIGITS AND UNIFORM-DISTRIBUTION MOD-1 ANNALS OF PROBABILITY Diaconis, P. 1977; 5 (1): 72-81
  • EXAMPLES FOR THEORY OF INFINITE ITERATION OF SUMMABILITY METHODS CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES Diaconis, P. 1977; 29 (3): 489-497
  • BUFFONS PROBLEM WITH A LONG NEEDLE JOURNAL OF APPLIED PROBABILITY Diaconis, P. 1976; 13 (3): 614-618
  • Protocol Issues in Randomized Clinical Trials of a Surgical Treatment of Duodenal Ulcer Costs, Risks and Benefits of Surgery Diaconis, P. edited by Bunker, J., Barnes, B., Mosteller, F. Oxford University Press. 1976