![Persi Diaconis](https://profiles.stanford.edu/proxy/api/cap/profiles/10463/resources/profilephoto/350x350.1509532792277.jpg)
Persi Diaconis
Mary V. Sunseri Professor in the School of Humanities and Sciences and Professor of Mathematics
Statistics
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.
Administrative Appointments
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Visiting Professor, Université de Nice-Sophia Antipolis (2006 - 2007)
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Fellow, Center for Advanced Study in the Behavioral Sciences (1999 - 2000)
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Mary Sunseri Professor, Department of Statistics, Stanford University (1998 - Present)
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Professor of Mathematics, Stanford University (1998 - Present)
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David Duncan Professor, Department of Mathematics and ORIE, Cornell University (1996 - 1998)
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George Vasmer Leverett Professor of Mathematics, Harvard University (1987 - 1997)
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Visiting Professor, Department of Mathematics, Harvard University (1985 - 1986)
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Visiting Professor, Department of Mathematics, Massachusetts Institute of Technology (1985 - 1986)
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Professor of Statistics, Stanford University (1981 - 1987)
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Visiting Professor, Department of Statistics, Harvard University (1981 - 1982)
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Associate Professor of Statistics, Stanford University (1979 - 1980)
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Research Staff Member, AT&T Bell Laboratories (1978 - 1979)
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Assistant Professor of Statistics, Stanford University (1974 - 1979)
Program Affiliations
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Symbolic Systems Program
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.
2024-25 Courses
- Introduction to Combinatorics and Its Applications
MATH 108 (Spr) - Theory of Probability I
MATH 230A, STATS 310A (Aut) - Topics in Combinatorics
MATH 233C (Spr) -
Independent Studies (3)
- Advanced Reading and Research
MATH 360 (Aut, Win, Spr) - Industrial Research for Statisticians
STATS 398 (Aut, Win, Spr) - Research
STATS 399 (Aut, Win, Spr)
- Advanced Reading and Research
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Prior Year Courses
2023-24 Courses
- Functions of a Complex Variable
MATH 106 (Win) - Modern Markov Chains
MATH 235, STATS 318 (Win) - Theory of Probability I
MATH 230A, STATS 310A (Aut)
2021-22 Courses
- Elementary Theory of Numbers
MATH 152 (Win) - Theory of Probability I
MATH 230A, STATS 310A (Aut) - Topics in Representation Theory
MATH 263A (Aut)
- Functions of a Complex Variable
Stanford Advisees
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Doctoral Dissertation Reader (AC)
Rahul Raphael Kanekar -
Doctoral Dissertation Advisor (AC)
Michael Howes, Zhiqi Li, Milo Marsden, Nathan Tung -
Orals Evaluator
June Vuong
All Publications
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Enumerative theory for the Tsetlin library
JOURNAL OF ALGEBRA
2024; 655: 139-162
View details for DOI 10.1016/j.jalgebra.2023.08.009
View details for Web of Science ID 001252306200001
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Isomorphisms between random graphs
JOURNAL OF COMBINATORIAL THEORY SERIES B
2023; 160: 144-162
View details for DOI 10.1016/j.jctb.2023.01.001
View details for Web of Science ID 001003656600001
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SEQUENTIAL IMPORTANCE SAMPLING FOR ESTIMATING EXPECTATIONS OVER THE SPACE OF PERFECT MATCHINGS
ANNALS OF APPLIED PROBABILITY
2023; 33 (2): 799-833
View details for DOI 10.1214/22-AAP1834
View details for Web of Science ID 000960867800006
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In Praise (and Search) of J. V. Uspensky
ENERGY AND BUILDINGS
2023; 282: 160-183
View details for DOI 10.1214/22-STS866
View details for Web of Science ID 000991879600010
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Double coset Markov chains
FORUM OF MATHEMATICS SIGMA
2023; 11
View details for DOI 10.1017/fms.2022.106
View details for Web of Science ID 000908038100001
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Approximate exchangeability and de Finetti priors in 2022
SCANDINAVIAN JOURNAL OF STATISTICS
2022
View details for DOI 10.1111/sjos.12609
View details for Web of Science ID 000865096600001
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Shuffling cards by spatial motion
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
2022; 152: 149-176
View details for DOI 10.1016/j.spa.2022.06.023
View details for Web of Science ID 000828309400004
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Statistical enumeration of groups by double cosets
JOURNAL OF ALGEBRA
2022; 607: 214-246
View details for DOI 10.1016/j.jalgebra.2021.05.010
View details for Web of Science ID 000833526600009
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Gambler's Ruin and the ICM
STATISTICAL SCIENCE
2022; 37 (3): 289-305
View details for DOI 10.1214/21-STS826
View details for Web of Science ID 000851465300001
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Guessing about Guessing: Practical Strategies for Card Guessing with Feedback
AMERICAN MATHEMATICAL MONTHLY
2022
View details for DOI 10.1080/00029890.2022.2069986
View details for Web of Science ID 000799164200001
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Partial Exchangeability for Contingency Tables
MATHEMATICS
2022; 10 (3)
View details for DOI 10.3390/math10030442
View details for Web of Science ID 000756374000001
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A PHASE TRANSITION FOR REPEATED AVERAGES
ANNALS OF PROBABILITY
2022; 50 (1): 1-17
View details for DOI 10.1214/21-AOP1526
View details for Web of Science ID 000760718500001
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Card guessing with partial feedback
COMBINATORICS PROBABILITY & COMPUTING
2022; 31 (1): 1-20
View details for DOI 10.1017/S0963548321000134
View details for Web of Science ID 000889141300001
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Randomized sequential importance sampling for estimating the number of perfect matchings in bipartite graphs
ADVANCES IN APPLIED MATHEMATICS
2021; 131
View details for DOI 10.1016/j.aam.2021.102247
View details for Web of Science ID 000701880400008
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Hahn polynomials and the Burnside process
RAMANUJAN JOURNAL
2021
View details for DOI 10.1007/s11139-021-00482-z
View details for Web of Science ID 000696746300001
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Speeding up Markov chains with deterministic jumps (vol 178, pg 1193, 2020)
PROBABILITY THEORY AND RELATED FIELDS
2021
View details for DOI 10.1007/s00440-021-01049-1
View details for Web of Science ID 000692971000001
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Discussion of "A Gibbs Sampler for a Class of Random Convex Polytopes"
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
2021; 116 (535): 1193-1195
View details for DOI 10.1080/01621459.2021.1950000
View details for Web of Science ID 000796973100012
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The-Square-and-Add Markov Chain
MATHEMATICAL INTELLIGENCER
2021
View details for DOI 10.1007/s00283-021-10058-w
View details for Web of Science ID 000652440400001
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Permanental generating functions and sequential importance sampling
ADVANCES IN APPLIED MATHEMATICS
2021; 126
View details for DOI 10.1016/j.aam.2019.05.004
View details for Web of Science ID 000625385000016
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RANDOM WALK ON UNIPOTENT MATRIX GROUPS
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE
2021; 54 (3): 587-625
View details for DOI 10.24033/asens.2466
View details for Web of Science ID 000709109400002
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GAMBLER'S RUIN ESTIMATES ON FINITE INNER UNIFORM DOMAINS
ANNALS OF APPLIED PROBABILITY
2021; 31 (2): 865-895
View details for DOI 10.1214/20-AAP1607
View details for Web of Science ID 000664792400012
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Tensor product Markov chains
JOURNAL OF ALGEBRA
2020; 561: 17–83
View details for DOI 10.1016/j.jalgebra.2019.10.038
View details for Web of Science ID 000560726700003
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Speeding up Markov chains with deterministic jumps
PROBABILITY THEORY AND RELATED FIELDS
2020
View details for DOI 10.1007/s00440-020-01006-4
View details for Web of Science ID 000572039300002
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Analytic-geometric methods for finite Markov chains with applications to quasi-stationarity
ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS
2020; 17 (2): 901–91
View details for DOI 10.30757/ALEA.v17-35
View details for Web of Science ID 000604979900011
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Reproducing kernel orthogonal polynomials on the multinomial distribution
JOURNAL OF APPROXIMATION THEORY
2019; 242: 1–30
View details for DOI 10.1016/j.jat.2019.01.007
View details for Web of Science ID 000468713900001
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THE SAMPLE SIZE REQUIRED IN IMPORTANCE SAMPLING
ANNALS OF APPLIED PROBABILITY
2018; 28 (2): 1099–1135
View details for DOI 10.1214/17-AAP1326
View details for Web of Science ID 000431722900011
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Bayesian goodness of fit tests: a conversation for David Mumford
ANNALS OF MATHEMATICAL SCIENCES AND APPLICATIONS
2018; 3 (1): 287–308
View details for Web of Science ID 000435089900010
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A CENTRAL LIMIT THEOREM FOR A NEW STATISTIC ON PERMUTATIONS
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS
2017; 48 (4): 561–73
View details for DOI 10.1007/s13226-017-0246-3
View details for Web of Science ID 000419195300006
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UNIVERSAL LIMIT THEOREMS IN GRAPH COLORING PROBLEMS WITH CONNECTIONS TO EXTREMAL COMBINATORICS
ANNALS OF APPLIED PROBABILITY
2017; 27 (1): 337-394
View details for DOI 10.1214/16-AAP1205
View details for Web of Science ID 000397363200011
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Useful Bounds on the Extreme Eigenvalues and Vectors of Matrices for Harper's Operators
LARGE TRUNCATED TOEPLITZ MATRICES, TOEPLITZ OPERATORS, AND RELATED TOPICS: THE ALBRECHT BOTTCHER ANNIVERSARY VOLUME
2017; 259: 235–65
View details for Web of Science ID 000417893200014
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The Mathematics of the Flip and Horseshoe Shuffles
AMERICAN MATHEMATICAL MONTHLY
2016; 123 (6): 542-556
View details for DOI 10.4169/amer.math.monthly.123.6.542
View details for Web of Science ID 000381754900002
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Estimates on the amplitude of the first Dirichlet eigenvector in discrete frameworks
SCIENCE CHINA-MATHEMATICS
2016; 59 (2): 205-226
View details for DOI 10.1007/s11425-015-5085-2
View details for Web of Science ID 000369949400001
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Central limit theorems for some set partition statistics
ADVANCES IN APPLIED MATHEMATICS
2015; 70: 92-105
View details for DOI 10.1016/j.aam.2015.06.008
View details for Web of Science ID 000361255600006
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de Finetti Priors using Markov chain Monte Carlo computations
STATISTICS AND COMPUTING
2015; 25 (4): 797-808
Abstract
Recent advances in Monte Carlo methods allow us to revisit work by de Finetti who suggested the use of approximate exchangeability in the analyses of contingency tables. This paper gives examples of computational implementations using Metropolis Hastings, Langevin and Hamiltonian Monte Carlo to compute posterior distributions for test statistics relevant for testing independence, reversible or three way models for discrete exponential families using polynomial priors and Gröbner bases.
View details for DOI 10.1007/s11222-015-9562-9
View details for Web of Science ID 000356828600009
View details for PubMedCentralID PMC4578810
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de Finetti Priors using Markov chain Monte Carlo computations.
Statistics and computing
2015; 25 (4): 797-808
Abstract
Recent advances in Monte Carlo methods allow us to revisit work by de Finetti who suggested the use of approximate exchangeability in the analyses of contingency tables. This paper gives examples of computational implementations using Metropolis Hastings, Langevin and Hamiltonian Monte Carlo to compute posterior distributions for test statistics relevant for testing independence, reversible or three way models for discrete exponential families using polynomial priors and Gröbner bases.
View details for DOI 10.1007/s11222-015-9562-9
View details for PubMedID 26412947
View details for PubMedCentralID PMC4578810
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An introduction to multivariate Krawtchouk polynomials and their applications
JOURNAL OF STATISTICAL PLANNING AND INFERENCE
2014; 154: 39-53
View details for DOI 10.1016/j.jspi.2014.02.004
View details for Web of Science ID 000343348700005
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Carries, Group Theory, and Additive Combinatorics
AMERICAN MATHEMATICAL MONTHLY
2014; 121 (8): 674-688
View details for DOI 10.4169/amer.math.monthly.121.08.674
View details for Web of Science ID 000343376800002
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Unseparated pairs and fixed points in random permutations
ADVANCES IN APPLIED MATHEMATICS
2014; 61: 102-124
View details for DOI 10.1016/j.aam.2014.05.006
View details for Web of Science ID 000344435400006
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Combinatorics of balanced carries
ADVANCES IN APPLIED MATHEMATICS
2014; 59: 8-25
View details for DOI 10.1016/j.aam.2014.05.005
View details for Web of Science ID 000340331600002
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Convolution powers of complex functions on Z
MATHEMATISCHE NACHRICHTEN
2014; 287 (10): 1106-1130
View details for DOI 10.1002/mana.201200163
View details for Web of Science ID 000339011500003
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Hopf algebras and Markov chains: two examples and a theory
JOURNAL OF ALGEBRAIC COMBINATORICS
2014; 39 (3): 527-585
View details for DOI 10.1007/s10801-013-0456-7
View details for Web of Science ID 000333706100001
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Fluctuations of the Bose-Einstein condensate
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
2014; 47 (8)
View details for DOI 10.1088/1751-8113/47/8/085201
View details for Web of Science ID 000332003600002
- An Introduction to Multivariate Krawtchouck Polynomials and their Applications Journal of Statistical Planning and Inference 2014
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ESTIMATING AND UNDERSTANDING EXPONENTIAL RANDOM GRAPH MODELS
ANNALS OF STATISTICS
2013; 41 (5): 2428-2461
View details for DOI 10.1214/13-AOS1155
View details for Web of Science ID 000327746100006
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Some things we've learned (about Markov chain Monte Carlo)
BERNOULLI
2013; 19 (4): 1294-1305
View details for DOI 10.3150/12-BEJSP09
View details for Web of Science ID 000324346200009
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ANALYSIS OF CASINO SHELF SHUFFLING MACHINES
ANNALS OF APPLIED PROBABILITY
2013; 23 (4): 1692-1720
View details for DOI 10.1214/12-AAP884
View details for Web of Science ID 000321678200014
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Random doubly stochastic tridiagonal matrices
RANDOM STRUCTURES & ALGORITHMS
2013; 42 (4): 403-437
View details for DOI 10.1002/rsa.20452
View details for Web of Science ID 000319070400001
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Note on a partition limit theorem for rank and crank
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
2013; 45: 551-553
View details for DOI 10.1112/blms/bds121
View details for Web of Science ID 000318803500010
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Interval Graph Limits
ANNALS OF COMBINATORICS
2013; 17 (1): 27-52
Abstract
We work out a graph limit theory for dense interval graphs. The theory developed departs from the usual description of a graph limit as a symmetric function W (x, y) on the unit square, with x and y uniform on the interval (0, 1). Instead, we fix a W and change the underlying distribution of the coordinates x and y. We find choices such that our limits are continuous. Connections to random interval graphs are given, including some examples. We also show a continuity result for the chromatic number and clique number of interval graphs. Some results on uniqueness of the limit description are given for general graph limits.
View details for DOI 10.1007/s00026-012-0175-0
View details for Web of Science ID 000319358600003
View details for PubMedCentralID PMC4578824
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Interval Graph Limits.
Annals of combinatorics
2013; 17 (1): 27-52
Abstract
We work out a graph limit theory for dense interval graphs. The theory developed departs from the usual description of a graph limit as a symmetric function W (x, y) on the unit square, with x and y uniform on the interval (0, 1). Instead, we fix a W and change the underlying distribution of the coordinates x and y. We find choices such that our limits are continuous. Connections to random interval graphs are given, including some examples. We also show a continuity result for the chromatic number and clique number of interval graphs. Some results on uniqueness of the limit description are given for general graph limits.
View details for DOI 10.1007/s00026-012-0175-0
View details for PubMedID 26405368
View details for PubMedCentralID PMC4578824
- Sampling from a Manifold Advances in Modern Statistical Theory and Applications: A Festschrift in honor of Morris L. Eaton 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 2013
- Carries, Group Theory and Additive Combinatorics American Mathematical Monthly 2013
- Fluctuations of the Bose-Einstein Condensate Journal of Physics A: Mathematical and Theoretical 2013; 47 (8)
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Foulkes characters, Eulerian idempotents, and an amazing matrix
JOURNAL OF ALGEBRAIC COMBINATORICS
2012; 36 (3): 425-440
View details for DOI 10.1007/s10801-012-0343-7
View details for Web of Science ID 000308700600006
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Gibbs/Metropolis algorithms on a convex polytope
MATHEMATISCHE ZEITSCHRIFT
2012; 272 (1-2): 109-129
View details for DOI 10.1007/s00209-011-0924-5
View details for Web of Science ID 000308646500007
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A PROBABILISTIC INTERPRETATION OF THE MACDONALD POLYNOMIALS
ANNALS OF PROBABILITY
2012; 40 (5): 1861-1896
View details for DOI 10.1214/11-AOP674
View details for Web of Science ID 000311005600001
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On Dirichlet eigenvectors for neutral two-dimensional Markov chains
ELECTRONIC JOURNAL OF PROBABILITY
2012; 17: 1-41
View details for DOI 10.1214/EJP.v17-1830
View details for Web of Science ID 000307815700001
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EXCHANGEABLE PAIRS OF BERNOULLI RANDOM VARIABLES, KRAWTCHOUCK POLYNOMIALS, AND EHRENFEST URNS
AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS
2012; 54 (1): 81-101
View details for DOI 10.1111/j.1467-842X.2012.00654.x
View details for Web of Science ID 000306795200005
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Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
ADVANCES IN MATHEMATICS
2012; 229 (4): 2310-2337
View details for DOI 10.1016/j.aim.2011.12.024
View details for Web of Science ID 000300386600007
- On the spectral analysis of second-order Markov chains Annales de la Faculté des Sciences de Toulouse, Mathematiques 2012; 22: 573-621
- Riffle Shuffles with Biased Cuts Formal Power Series and Algebraic Combinatorics Conference 2012
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RANDOM GRAPHS WITH A GIVEN DEGREE SEQUENCE
ANNALS OF APPLIED PROBABILITY
2011; 21 (4): 1400-1435
View details for DOI 10.1214/10-AAP728
View details for Web of Science ID 000294220500006
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The Mathematics of Mixing Things Up
JOURNAL OF STATISTICAL PHYSICS
2011; 144 (3): 445-458
View details for DOI 10.1007/s10955-011-0284-x
View details for Web of Science ID 000294227400002
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Geometric analysis for the metropolis algorithm on Lipschitz domains
INVENTIONES MATHEMATICAE
2011; 185 (2): 239-281
View details for DOI 10.1007/s00222-010-0303-6
View details for Web of Science ID 000293978500001
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A RULE OF THUMB FOR RIFFLE SHUFFLING
ANNALS OF APPLIED PROBABILITY
2011; 21 (3): 843-875
View details for DOI 10.1214/10-AAP701
View details for Web of Science ID 000291736600002
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On Barycentric Subdivision
COMBINATORICS PROBABILITY & COMPUTING
2011; 20 (2): 213-237
View details for DOI 10.1017/S0963548310000441
View details for Web of Science ID 000287608000003
- Magical Mathematics: The Mathematical Ideas that Animate Great Magic Tricks Princeton University Press. 2011
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STOCHASTIC ALTERNATING PROJECTIONS
ILLINOIS JOURNAL OF MATHEMATICS
2010; 54 (3): 963-979
View details for Web of Science ID 000208398200006
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ON ADDING A LIST OF NUMBERS (AND OTHER ONE-DEPENDENT DETERMINANTAL PROCESSES)
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY
2010; 47 (4): 639-670
View details for Web of Science ID 000283966700002
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Functions of random walks on hyperplane arrangements
ADVANCES IN APPLIED MATHEMATICS
2010; 45 (3): 410-437
View details for DOI 10.1016/j.aam.2010.02.001
View details for Web of Science ID 000281294000009
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Threads Through Group Theory
International Conference on the Character Theory of Finite Groups, in Honor of I Martin Isaacs
AMER MATHEMATICAL SOC. 2010: 33–47
View details for Web of Science ID 000283112600004
- Geometric Analysis for the Metropolis Algorithm on Lipschitz Domains Inventiones Mathematicae 2010; 185 (2): 239-281
- Properties of Uniform Doubly Stochastic Matrices Annals of Applied Probability 2010
- Gibbs Sampling, Conjugate Priors and Coupling Sankhya 2010; 72-A (1): 136-169
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Carries, Shuffling, and an Amazing Matrix
AMERICAN MATHEMATICAL MONTHLY
2009; 116 (9): 788-803
View details for DOI 10.4169/000298909X474864
View details for Web of Science ID 000207893000002
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On Times to Quasi-stationarity for Birth and Death Processes
JOURNAL OF THEORETICAL PROBABILITY
2009; 22 (3): 558-586
View details for DOI 10.1007/s10959-009-0234-6
View details for Web of Science ID 000268192300002
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Carries, shuffling, and symmetric functions
ADVANCES IN APPLIED MATHEMATICS
2009; 43 (2): 176-196
View details for DOI 10.1016/j.aam.2009.02.002
View details for Web of Science ID 000267134700006
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Micro-local analysis for the Metropolis algorithm
MATHEMATISCHE ZEITSCHRIFT
2009; 262 (2): 411-447
View details for DOI 10.1007/s00209-008-0383-9
View details for Web of Science ID 000265442300010
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SUPERCHARACTER FORMULAS FOR PATTERN GROUPS
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
2009; 361 (7): 3501-3533
View details for Web of Science ID 000264881700006
- A Sequential Importance Sampling Algorithm for Generating Random Graphs With Prescribed Degrees Journal of Internet Mathematics 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 2009
- Threshold Graph Limits and Random Threshold Graphs Journal of Internet Mathematics 2009; 5 (3): 267-320
- Riffle shuffles of a deck with repeated cards 21st International Conference on Formal Power Series and Algebraic Combinatorics 2009: 89–102
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FASTEST MIXING MARKOV CHAIN ON GRAPHS WITH SYMMETRIES
SIAM JOURNAL ON OPTIMIZATION
2009; 20 (2): 792-819
View details for DOI 10.1137/070689413
View details for Web of Science ID 000268859300011
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On characterizations of Metropolis type algorithms in continuous time
ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS
2009; 6: 199-238
View details for Web of Science ID 000208169800009
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THE MARKOV CHAIN MONTE CARLO REVOLUTION
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY
2009; 46 (2): 179-205
View details for Web of Science ID 000263433700002
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HORSESHOES IN MULTIDIMENSIONAL SCALING AND LOCAL KERNEL METHODS
ANNALS OF APPLIED STATISTICS
2008; 2 (3): 777-807
View details for DOI 10.1214/08-AOAS165
View details for Web of Science ID 000261057900001
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On fixed points of permutations
JOURNAL OF ALGEBRAIC COMBINATORICS
2008; 28 (1): 189-218
View details for DOI 10.1007/s10801-008-0135-2
View details for Web of Science ID 000257489000010
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Gibbs sampling, exponential families and orthogonal polynomials
STATISTICAL SCIENCE
2008; 23 (2): 151-178
View details for DOI 10.1214/07-STS252
View details for Web of Science ID 000259275400001
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Supercharacters and superclasses for algebra groups
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
2008; 360 (5): 2359-2392
View details for Web of Science ID 000252879200005
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Threshold Graph Limits and Random Threshold Graphs.
Internet mathematics
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
- Comment: Gibbs Sampling, Exponential Families and Orthogonal Polynomials Statistical Science 2008; 23 (2): 179-182
- Projection Pursuit for Discrete Data Probability and Statistics: Essays in Honor of David A. Freedman Institute of Mathematical Statistics. 2008: 265–288
- Products of Universal Cycles A lifetime of puzzles: a collection of puzzles in honor of Martin Gardner edited by Demain, E., Demaine, M., Rodgers, T. AK Peters, Ltd.. 2008: 35–55
- Graph Limits and Exchangeable Random Graphs Rendiconti di Matematica 2008; VII (28): 33-61
- Comment Journal of the American Statistical Association 2008; 103 (481): 16
- Mathematical Statistics Princeton Companion to Mathematics edited by Gowers, T. Princeton University Press. 2008: 916-920
- Comment: Gibbs Sampling, Exponential Families and Orthogonal Polynomials Statistical Science 2008; 23 (2): 183-186
- Rejoinder: Gibbs Sampling, Exponential Families and Orthogonal Polynomials Statistical Science 2008; 23 (2): 196-200
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Shuffling Cards, Adding Numbers, and Symmetric Functions
19th ACM-SIAM Symposium on Discrete Algorithms
SIAM. 2008: 560–560
View details for Web of Science ID 000281596900062
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Dynamical bias in the coin toss
SIAM REVIEW
2007; 49 (2): 211-235
View details for DOI 10.1137/S0036144504446436
View details for Web of Science ID 000246858500002
- The Solutions to Elmsley's Problem Math Horizons 2007; 14: 22-27
- Hit and Run as a Unifying Device Journal de la Société Française de Statistique 2007; 148 (4): 5-28
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The fastest mixing Markov process on a graph and a connection to a maximum variance unfolding problem
SIAM REVIEW
2006; 48 (4): 681-699
View details for DOI 10.1137/S0036144504443821
View details for Web of Science ID 000242326500002
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Separation cut-offs for birth and death chains
ANNALS OF APPLIED PROBABILITY
2006; 16 (4): 2098-2122
View details for DOI 10.1214/105051606000000501
View details for Web of Science ID 000243782000014
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Bayesian analysis for reversible Markov chains
ANNALS OF STATISTICS
2006; 34 (3): 1270-1292
View details for DOI 10.1214/009053606000000290
View details for Web of Science ID 000239471300008
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Examples comparing importance sampling and the metropolis algorithm
ILLINOIS JOURNAL OF MATHEMATICS
2006; 50 (1): 67-91
View details for Web of Science ID 000242194700005
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Markov bases for noncommutative Fourier analysis of ranked data
Workshop on Computational Algebraic Statistics
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD. 2006: 182–95
View details for DOI 10.1016/j.jsc.2005.04.009
View details for Web of Science ID 000235394300007
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Fastest mixing Markov chain on a path
AMERICAN MATHEMATICAL MONTHLY
2006; 113 (1): 70-74
View details for Web of Science ID 000234776200007
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Sequential Monte Carlo methods for statistical analysis of tables
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
2005; 100 (469): 109-120
View details for DOI 10.1198/016214504000001303
View details for Web of Science ID 000233311100016
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Analysis of a Bose-Einstein Markov chain
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
2005; 41 (3): 409-418
View details for DOI 10.1016/j.anihpb.2004.09.007
View details for Web of Science ID 000229277300009
- Exchangeable Pairs and Poisson Approximation Probability Surveys 2005; 2 (1): 64-106
- Symmetry Analysis of Reversible Markov Chains Journal of Internet Mathematics 2005; 2 (1): 31-71
- What is...a Random Matrix Notices of the American Mathematical Society 2005; 52 (11): 1348-1349
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Fastest mixing Markov chain on a graph
SIAM REVIEW
2004; 46 (4): 667-689
View details for DOI 10.1137/s0036144503423264
View details for Web of Science ID 000225304300006
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A super-class walk on upper-triangular matrices
JOURNAL OF ALGEBRA
2004; 278 (2): 739-765
View details for DOI 10.1016/j.jalgebra.2004.04.005
View details for Web of Science ID 000222709400018
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Random matrices, magic squares and matching polynomials
ELECTRONIC JOURNAL OF COMBINATORICS
2004; 11 (2)
View details for Web of Science ID 000221826200002
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The Markov moment problem and de Finetti's theorem: Part I
MATHEMATISCHE ZEITSCHRIFT
2004; 247 (1): 183-199
View details for DOI 10.1007/s00209-003-0633-9
View details for Web of Science ID 000220713800008
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The Markov moment problem and de Finetti's theorem: Part II
MATHEMATISCHE ZEITSCHRIFT
2004; 247 (1): 201-212
View details for DOI 10.1007/s00209-003-0636-6
View details for Web of Science ID 000220713800009
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Numerical results for the metropolis algorithm
EXPERIMENTAL MATHEMATICS
2004; 13 (2): 207-213
View details for Web of Science ID 000222891900008
- Uses of Exchangeable Pairs in Monte Carlo Markov Chains Stein's Method: Expository Lectures and Applications 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 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 edited by Diaconis, P., Holmes, S. Institute of Mathematical Statistics. 2004: 27–43
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The Poisson-Dirichlet law is the unique invariant distribution for uniform split-merge transformations
ANNALS OF PROBABILITY
2004; 32 (1B): 915-938
View details for Web of Science ID 000220570400010
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New tests of the correspondence between unitary eigenvalues and the zeros of Riemann's zeta function
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
2003; 36 (12): 2883-2906
View details for Web of Science ID 000182454900003
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Patterns in eigenvalues: The 70th Josiah Willard Gibbs Lecture
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY
2003; 40 (2): 155-178
View details for Web of Science ID 000181708200001
- Brownian Motion and the Classical Groups Probability, Statistics and their applications: Papers in Honor of Rabii Bhattacharaya 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 edited by Campbell, C. M., Roberson, E. F., Smith, G. C. Oxford: Cambridge University Press. 2003: 120–142
- New Tests of the Correspondence Between Unitary Eigenvalues and the Zeros of Riemann's Zeta Functions Journal of Physics A: Mathematics and General 2003; 36 (12): 2883-2906
- The Problem of Thinking Too Much Bulletin of the American Academy of Arts and Sciences 2003; LVI (3): 26-38
- Mathematical Developments from the Analysis of Riffle-Shuffling Groups, Combinatorics and Geometry edited by Ivanov, A., Fuanou, A., Liebeck, M. World Scientific. 2003: 73–97
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G. H. Hardy and probability???
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
2002; 34: 385-402
View details for DOI 10.1112/S002460930200111X
View details for Web of Science ID 000176661300001
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The asymmetric one-dimensional constrained Ising model: Rigorous results
JOURNAL OF STATISTICAL PHYSICS
2002; 107 (5-6): 945-975
View details for Web of Science ID 000175853800001
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Toeplitz minors
JOURNAL OF COMBINATORIAL THEORY SERIES A
2002; 97 (2): 252-271
View details for DOI 10.1006/jcta.2001.3214
View details for Web of Science ID 000174102400004
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A different construction of Gaussian fields from Markov chains: Dirichlet covariances
BDI 2001 Conference
INST MATHEMATICAL STATISTICS. 2002: 863–78
View details for Web of Science ID 000179857800008
- Random Walk on Trees and Matchings Electronic Journal of Probability 2002; 7: 1-17
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Unitary correlations and the Fejer kernel - Dedicated to Harold Widom on his 70th birthday
MATHEMATICAL PHYSICS ANALYSIS AND GEOMETRY
2002; 5 (2): 101-123
View details for Web of Science ID 000180282100001
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A geometric interpretation of the Metropolis-Hastings algorithm
STATISTICAL SCIENCE
2001; 16 (4): 335-339
View details for Web of Science ID 000173928200003
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Combinatorics for the East model
ADVANCES IN APPLIED MATHEMATICS
2001; 27 (1): 192-206
View details for Web of Science ID 000169489700006
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Chutes and ladders in Markov chains
JOURNAL OF THEORETICAL PROBABILITY
2001; 14 (3): 899-926
View details for Web of Science ID 000171744500014
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Statistical problems involving permutations with restricted positions
Symposium on State of the Art in Probability and Statistics: Festschrift for Willem R VanZwet
INST MATHEMATICAL STATISTICS. 2001: 195–222
View details for Web of Science ID 000175458600011
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Linear functionals of eigenvalues of random matrices
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
2001; 353 (7): 2615-2633
View details for Web of Science ID 000168039100003
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Analysis of a nonreversible Markov chain sampler
ANNALS OF APPLIED PROBABILITY
2000; 10 (3): 726-752
View details for Web of Science ID 000166779900003
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Immanants and finite point processes
JOURNAL OF COMBINATORIAL THEORY SERIES A
2000; 91 (1-2): 305-321
View details for Web of Science ID 000089261700014
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Bounds for Kac's master equation
COMMUNICATIONS IN MATHEMATICAL PHYSICS
2000; 209 (3): 729-755
View details for Web of Science ID 000085957000006
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Analysis of systematic scan metropolis algorithms using Iwahori-Hecke algebra techniques
MICHIGAN MATHEMATICAL JOURNAL
2000; 48: 157-190
View details for Web of Science ID 000172971000008
- A Bayesian Peek into Feller I Sankhya A 2000; 64 (3): 820-841
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Longest increasing subsequences: From patience sorting to the Baik-Deift-Johansson theorem
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY
1999; 36 (4): 413-432
View details for Web of Science ID 000082398900001
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Random walks and plane arrangements in three dimensions
AMERICAN MATHEMATICAL MONTHLY
1999; 106 (6): 502-524
View details for Web of Science ID 000080427600002
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Iterated random functions
SIAM REVIEW
1999; 41 (1): 45-76
View details for Web of Science ID 000079557300002
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Matchings and phylogenetic trees
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
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
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Consistency of Bayes estimates for nonparametric regression: normal theory
BERNOULLI
1998; 4 (4): 411-444
View details for Web of Science ID 000084941500001
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A place for philosophy? The rise of modeling in statistical science
International Symposium on Current and Future Challenges in Aoolied Mathematics, to Mark the 50th Anniversary of the Division-of-Applied-Mathematics
UNIV PRESS INC. 1998: 797–805
View details for Web of Science ID 000078412100013
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Walks on generating sets of groups
INVENTIONES MATHEMATICAE
1998; 134 (2): 251-299
View details for Web of Science ID 000076754700002
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Random walks and hyperplane arrangements
ANNALS OF PROBABILITY
1998; 26 (4): 1813-1854
View details for Web of Science ID 000079193400017
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What do we know about the metropolis algorithm?
27th Annual ACM Symposium on Theory of Computing
ACADEMIC PRESS INC ELSEVIER SCIENCE. 1998: 20–36
View details for Web of Science ID 000075979500003
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Algebraic algorithms for sampling from conditional distributions
ANNALS OF STATISTICS
1998; 26 (1): 363-397
View details for Web of Science ID 000079135300014
- Random Walk and Hyperplane Arrangements Annals of Probability 1998; 26 (4): 1813-1854
- From Shuffling Cards to Walking Around the Building. An Introduction to Markov Chain Theory Proc. Int. Congress, Berlin 1998: 187–204
- Magic Routledge Encyclopedia of Philosophy edited by Craig, E. Routledge. 1998
- Lattice Walks and Primary Decomposition Mathematical Essays in Honor of Gian-Carlo Rota edited by Sagan, B., Stanley, R. P. 1998: 173–194
- The Graph of Generating Sets of an Abelian Group Colloquium Mathematicum 1998: 31-38
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Are there still things to do in Bayesian statistics?
Conference on Probability, Dynamics and Causality
KLUWER ACADEMIC PUBL. 1997: 5–18
View details for Web of Science ID 000071894300002
- Consistency of Bayes Estimates for Non-Parametric Regression: A Review Festschrift for Lucien LeCam edited by Pollard, D., Torgersen, E., Yang, G. L. New York: Springer. 1997: 157–166
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Walks on generating sets of Abelian groups
PROBABILITY THEORY AND RELATED FIELDS
1996; 105 (3): 393-421
View details for Web of Science ID A1996UV42000004
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Nash inequalities for finite Markov chains
JOURNAL OF THEORETICAL PROBABILITY
1996; 9 (2): 459-510
View details for Web of Science ID A1996UH44600012
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The cutoff phenomenon in finite Markov chains
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
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 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 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 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 1996; 6: 695-750
- Metrics on Compositions and Coincidences Among Renewal Sequences Random Discrete Structures edited by Aldous, D., Pemantle, R. New York: Springer Verlag. 1996: 81–102
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Primitive partition identities
International Combinatorics Colloquium, in Honor of Paul Erdos 80th Birthday
BOLYAI JANOS MATEMATIKA TARSULAT. 1996: 173–192
View details for Web of Science ID A1996BG86H00005
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HAMMERSLEYS INTERACTING PARTICLE PROCESS AND LONGEST INCREASING SUBSEQUENCES
PROBABILITY THEORY AND RELATED FIELDS
1995; 103 (2): 199-213
View details for Web of Science ID A1995TA22100003
- What Do We Know About the Metropolis Algorithm? Proceedings of the 27th Symposium on Theory of Computing 1995: 112–129
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RIFFLE SHUFFLES, CYCLES, AND DESCENTS
COMBINATORICA
1995; 15 (1): 11-29
View details for Web of Science ID A1995RT93500002
- An Application of Harnack Inequalities to Random Walk on Nilpotent Quotients Journal Fourier Analysis and Applications 1995: 189-207
- NonParametric Binary Regression with Random Covariates Probability and Mathematical Statistics 1995; 15: 243-273
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GRAY CODES FOR RANDOMIZATION PROCEDURES
STATISTICS AND COMPUTING
1994; 4 (4): 287-302
View details for Web of Science ID A1994PW03200009
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ON THE EIGENVALUES OF RANDOM MATRICES
JOURNAL OF APPLIED PROBABILITY
1994; 31A: 49-62
View details for Web of Science ID A1994NX79600007
- Three Examples of the Markov Chain Monte Carlo Method Discrete Probability and Algorithms edited by Aldous, D., Saloff-Coste, L., Spencer, J., Steele, J. M. New York: Springer-Verlag. 1994: 43–56
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MODERATE GROWTH AND RANDOM-WALK ON FINITE-GROUPS
GEOMETRIC AND FUNCTIONAL ANALYSIS
1994; 4 (1): 1-36
View details for Web of Science ID A1994NE69900001
- Rectangular Arrays With Fixed Margins Discrete Probability and Algorithms edited by Aldous, D., Saloff-Coste, L., Spencer, J., Steele, J. M. New York: Springer-Verlag. 1994: 15–42
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SPECTRAL-ANALYSIS FOR DISCRETE LONGITUDINAL DATA
ADVANCES IN MATHEMATICS
1994; 103 (1): 107-128
View details for Web of Science ID A1994MU99200002
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NONPARAMETRIC BINARY REGRESSION - A BAYESIAN-APPROACH
ANNALS OF STATISTICS
1993; 21 (4): 2108-2137
View details for Web of Science ID A1993MQ47700022
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COMPARISON TECHNIQUES FOR RANDOM-WALK ON FINITE-GROUPS
ANNALS OF PROBABILITY
1993; 21 (4): 2131-2156
View details for Web of Science ID A1993MP50200015
- Comparison Theorems for Reversible Markov Chains Annals of Applied Probability 1993; 3 (3): 696-730
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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
1993; 55 (1): 53-102
View details for Web of Science ID A1993KL31400004
- Non-Parametric Binary Bayesian Regression: A Bayesian Approach Annals of Statistics 1993; 21: 2018-2137
- Foreward Probability Models and Statistical Analyses For Ranking Data 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 edited by Finkelstein, L., Kantor, W. Center for Discrete Mathematics and Theoretical Computer Science. 1993: 87–104
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UNIVERSAL CYCLES FOR COMBINATORIAL STRUCTURES
DISCRETE MATHEMATICS
1992; 110 (1-3): 43-59
View details for Web of Science ID A1992KE90400005
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BINOMIAL COEFFICIENT CODES OVER GF(2)
DISCRETE MATHEMATICS
1992; 106: 181-188
View details for Web of Science ID A1992JM73800023
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AN AFFINE WALK ON THE HYPERCUBE
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
1992; 41 (1-2): 215-235
View details for Web of Science ID A1992JK69500020
- Analysis of Top to Random Shuffles Combinatorics, Probability and Computing 1992; 1: 135-155
- Non Parametric Binary Bayesian Regression Festschrift for Raj Bahaduhr Indian Statistical Institute. 1992
- Eigen-Analysis for Some Examples of the Metropolis Algorithm Contemporary Mathematics 1992; 138: 99-117
- Trailing the Dovetail Shuffle to its Lair Annals of Applied Probablity 1992; 2 (2): 294-313
- Sufficiency as Statistical Symmetry Proceedings of the 100th Anniversary Americal Mathematical Society 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 1992; 19: 298-315
- A Growth Model, A Game, An Algebra, Lagrange Inversion and Characteristic Classes Recondita Mathematics 1991; 49: 95-119
- Closed Form Summation for Classical Distributions: Variations on a Theme of Demoivre Statistical Science 1991; 61 (3): 284-302
- Geometric Bounds for Eigenvalues of Markov Chains Annals of Applied Probability 1991; 1 (1): 36-61
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STRONG STATIONARY TIMES VIA A NEW FORM OF DUALITY
ANNALS OF PROBABILITY
1990; 18 (4): 1483-1522
View details for Web of Science ID A1990EH57900003
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ON THE UNIFORM CONSISTENCY OF BAYES ESTIMATES FOR MULTINOMIAL PROBABILITIES
ANNALS OF STATISTICS
1990; 18 (3): 1317-1327
View details for Web of Science ID A1990DV56700017
- Finite Fourier Methods: Access to Tols Probabalistic combinatorics, Proceedings of Symposia in Applied Mathematics 1990: 171–194
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CAUCHYS EQUATION AND DEFINETTIS THEOREM
SCANDINAVIAN JOURNAL OF STATISTICS
1990; 17 (3): 235-250
View details for Web of Science ID A1990EP37700005
- Applications of Groups Representations to Statistical Problems Proceedings International Congress of Mathematician, Kyoto 1990: 1037–1048
- Asymptotic Analysis of a Random Walk on a Hypercube with Many Dimensions Random Structures and Algorithms 1990; 1: 51-72
- Efficient Computation of the Fourier Transform on Finite Groups Journal of the American Mathematical Society 1990; 3 (2): 297-332
- Patterned Matrices Matrix Theory and Applications: Proceedings of Symposia in Applied Mathematics, American Mathematical Society 1990: 37–58
- Bounds for Tail Probabilities of Weighted Sums of Independent Gamma Random Variables Topics in Statistical Dependence 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 1990; 4: 157-180
- Cauchy's Equation and de Finetti's Theorem Journal of Statistics 1990; 17 (3): 235-250
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METHODS FOR STUDYING COINCIDENCES
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
1989; 84 (408): 853-861
View details for Web of Science ID A1989CD46300001
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THE 1987 WALD MEMORIAL LECTURES - A GENERALIZATION OF SPECTRAL-ANALYSIS WITH APPLICATION TO RANKED DATA
ANNALS OF STATISTICS
1989; 17 (3): 949-979
View details for Web of Science ID A1989AV32100001
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FAIR DICE
AMERICAN MATHEMATICAL MONTHLY
1989; 96 (4): 337-339
View details for Web of Science ID A1989U246000005
- Bounds for Tail Probabilities of Weighted Sums of Independent Gamma Random Variables Symposium on Dependence in Statistics and Probability 1989: 147–166
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ON MERGING OF PROBABILITIES
SANKHYA-THE INDIAN JOURNAL OF STATISTICS SERIES A
1988; 50: 363-380
View details for Web of Science ID A1988U787800004
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HONEST BERNOULLI EXCURSIONS
JOURNAL OF APPLIED PROBABILITY
1988; 25 (3): 464-477
View details for Web of Science ID A1988Q629500002
- Application of the Method of Moments in Probability and Statistics Moments in Mathematics Proceedings of Symposia in Applied Mathematics, American Mathematical Society 1988: 125–142
- Conditional Limit Theorems for Exponential Families with Uniform Asymptotic Estimates and Applications to de Finetti's Theorem Theoretical Probability 1988; 1: 381-410
- Recent Progress in de Finetti's Notions of Exchangeability Bayesian Statistics 3: Proceedings of the Third Valencia International Meeting 1988: 111–125
- Bayesian Numerical Analysis Statistical Decision Theory and Related Topics IV edited by Berger, J., Gupta, S. New York: Springer-Verlag. 1988: 163–175
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INEQUALITIES FOR LINEAR-COMBINATIONS OF GAMMA-RANDOM VARIABLES
CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE
1987; 15 (4): 387-395
View details for Web of Science ID A1987N113000008
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WHAT IS AN ANALYSIS OF VARIANCE - DISCUSSION
ANNALS OF STATISTICS
1987; 15 (3): 917-921
View details for Web of Science ID A1987K140600005
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RANDOM-WALKS ARISING IN RANDOM NUMBER GENERATION
ANNALS OF PROBABILITY
1987; 15 (3): 1148-1165
View details for Web of Science ID A1987J563000020
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STRONG UNIFORM TIMES AND FINITE RANDOM-WALKS
ADVANCES IN APPLIED MATHEMATICS
1987; 8 (1): 69-97
View details for Web of Science ID A1987G271000005
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TIME TO REACH STATIONARITY IN THE BERNOULLI LAPLACE DIFFUSION-MODEL
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
1987; 18 (1): 208-218
View details for Web of Science ID A1987F785700016
- 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 Academic Press. 1987: 103–125
- Fred Mosteller as a Mathematical Statistician A Statistical Model 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 1987; 1: 15-32
- Projection Pursuit for Discrete Data Scandinavian Journal of Statistics 1987
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A DOZEN DE FINETTI-STYLE RESULTS IN SEARCH OF A THEORY
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
1987; 23: 397-423
View details for Web of Science ID A1987H929700008
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ON SQUARE ROOTS OF THE UNIFORM-DISTRIBUTION ON COMPACT-GROUPS
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
1986; 98 (2): 341-348
View details for Web of Science ID A1986E191700029
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SHUFFLING CARDS AND STOPPING-TIMES
AMERICAN MATHEMATICAL MONTHLY
1986; 93 (5): 333-348
View details for Web of Science ID A1986C129400001
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ON THE CONSISTENCY OF BAYES ESTIMATES - REJOINDER
ANNALS OF STATISTICS
1986; 14 (1): 63-67
View details for Web of Science ID A1986C196800013
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ON THE CONSISTENCY OF BAYES ESTIMATES
ANNALS OF STATISTICS
1986; 14 (1): 1-26
View details for Web of Science ID A1986C196800001
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ON INCONSISTENT BAYES ESTIMATES OF LOCATION
ANNALS OF STATISTICS
1986; 14 (1): 68-87
View details for Web of Science ID A1986C196800014
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AN ELEMENTARY PROOF OF STIRLING FORMULA
AMERICAN MATHEMATICAL MONTHLY
1986; 93 (2): 123-125
View details for Web of Science ID A1986AYZ5100008
- Products of Random Matrices and Computer Image Generation Contemporary Mathematics 1986; 50: 173-182
- Products of Random Matrices as They Arise in the Study of Random Walks on Groups Contemporary Mathematics 1986; 50: 183-195
- Applications of Nonommutative Fourier Analysis to Probability Problems Ecolé d' Été de Probabilites de St. Flours, XV-XVII, Springer Lecture Notes in Mathematics Berlin: Springer-Verlag. 1986: 51–100
- A Subjective Guide to Objective Chance Statistical Science 1986; 1: 171-174
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THE RADON-TRANSFORM ON Z2K
PACIFIC JOURNAL OF MATHEMATICS
1985; 118 (2): 323-345
View details for Web of Science ID A1985AKA9200009
- Bayesian Statistics as Honest Work Proceedings of the Berkeley Conference in Honor of Jerzey Neyman and Jack Kiefer 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 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 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 edited by Bernardo, J. M., Degroot, M. H., Lindley, D. V., Smith, A. F. 1985: 133–156
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TESTING FOR INDEPENDENCE IN A 2-WAY TABLE - NEW INTERPRETATIONS OF THE CHI-SQUARE STATISTIC
ANNALS OF STATISTICS
1985; 13 (3): 845-874
View details for Web of Science ID A1985AST9500001
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TESTING FOR INDEPENDENCE IN A 2-WAY TABLE - NEW INTERPRETATIONS OF THE CHI-SQUARE STATISTIC - REJOINDER
ANNALS OF STATISTICS
1985; 13 (3): 905-913
View details for Web of Science ID A1985AST9500012
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PROJECTION PURSUIT - DISCUSSION
ANNALS OF STATISTICS
1985; 13 (2): 494-496
View details for Web of Science ID A1985AKQ9500007
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ON NONLINEAR FUNCTIONS OF LINEAR-COMBINATIONS
SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING
1984; 5 (1): 175-191
View details for Web of Science ID A1984SF60000013
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ASYMPTOTICS OF GRAPHICAL PROJECTION PURSUIT
ANNALS OF STATISTICS
1984; 12 (3): 793-815
View details for Web of Science ID A1984TJ80600001
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ON INCONSISTENT BAYES ESTIMATES IN THE DISCRETE CASE
ANNALS OF STATISTICS
1983; 11 (4): 1109-1118
View details for Web of Science ID A1983RV59700008
- M and N plots Recent Advances in Statistics 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 edited by Box, G., Leonard, T., Wu, C. F. New York: Academic Press. 1983: 105–115
- The Mathematics of Perfect Shuffles Advances in Applied Mathematics 1983; 4 (2): 175-196
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COMPUTER-INTENSIVE METHODS IN STATISTICS
SCIENTIFIC AMERICAN
1983; 248 (5): 116-?
View details for Web of Science ID A1983QL31500013
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ON THE MAXIMUM DIFFERENCE BETWEEN THE EMPIRICAL AND EXPECTED HISTOGRAMS FOR SUMS
PACIFIC JOURNAL OF MATHEMATICS
1982; 100 (2): 287-327
View details for Web of Science ID A1982PG41100005
- Bayes Rules for Location Problems Statistical Decision Theory and Related Topics III edited by Gupta, S., Berger, J. 1982: 315–327
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ON THE DIFFERENCE BETWEEN THE EMPIRICAL HISTOGRAM AND THE NORMAL CURVE, FOR SUMS .2.
PACIFIC JOURNAL OF MATHEMATICS
1982; 100 (2): 359-371
View details for Web of Science ID A1982PG41100007
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VARIABLES ON SCATTERPLOTS LOOK MORE HIGHLY CORRELATED WHEN THE SCALES ARE INCREASED
SCIENCE
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
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UPDATING SUBJECTIVE-PROBABILITY
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
1982; 77 (380): 822-830
View details for Web of Science ID A1982PV60500019
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DE FINETTIS THEOREM FOR SYMMETRIC LOCATION FAMILIES
ANNALS OF STATISTICS
1982; 10 (1): 184-189
View details for Web of Science ID A1982NG05200014
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ON THE MODE OF AN EMPIRICAL HISTOGRAM FOR SUMS
PACIFIC JOURNAL OF MATHEMATICS
1982; 100 (2): 373-385
View details for Web of Science ID A1982PG41100008
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ON INCONSISTENT M-ESTIMATORS
ANNALS OF STATISTICS
1982; 10 (2): 454-461
View details for Web of Science ID A1982NV35500010
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ON THE STATISTICS OF VISION - THE JULESZ CONJECTURE
JOURNAL OF MATHEMATICAL PSYCHOLOGY
1981; 24 (2): 112-138
View details for Web of Science ID A1981MW68200002
- Magical Thinking in the Analysis of Scientific Data Annals of the New York Academy of Science 1981; 364: 236-244
- Partial Exchangeability and Sufficiency Proceedings of the Indian Statistical Institute Golden Jubilee International Conference on Statistics: Applications and New Directions 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 1981; 2: 121-137
- How Fast is the Fastest Fourier Transform Computer Science and Statistics: Proceedings of the 13th Symposium on the Interface edited by Eddy, W. F. 1981
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ON THE HISTOGRAM AS A DENSITY ESTIMATOR - L2 THEORY
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE
1981; 57 (4): 453-476
View details for Web of Science ID A1981MJ08100002
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THE ANALYSIS OF SEQUENTIAL EXPERIMENTS WITH FEEDBACK TO SUBJECTS
ANNALS OF STATISTICS
1981; 9 (1): 3-23
View details for Web of Science ID A1981LA53000002
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THE PERSISTENCE OF COGNITIVE ILLUSIONS
BEHAVIORAL AND BRAIN SCIENCES
1981; 4 (3): 333-334
View details for Web of Science ID A1981MN23200004
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ON THE MAXIMUM DEVIATION BETWEEN THE HISTOGRAM AND THE UNDERLYING DENSITY
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE
1981; 58 (2): 139-167
View details for Web of Science ID A1981MS56800001
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GENERATING A RANDOM PERMUTATION WITH RANDOM TRANSPOSITIONS
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE
1981; 57 (2): 159-179
View details for Web of Science ID A1981MB74300001
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FINITE EXCHANGEABLE SEQUENCES
ANNALS OF PROBABILITY
1980; 8 (4): 745-764
View details for Web of Science ID A1980KE73300006
- Average Running Time of the Fast Fourier Transform Journal of Algorithms 1980; 1 (2): 187-208
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DE FINETTI THEOREM FOR MARKOV-CHAINS
ANNALS OF PROBABILITY
1980; 8 (1): 115-130
View details for Web of Science ID A1980JK96700005
- de Finetti's Generalizations of Exchangeability Studies in Inductive Logic and Probability edited by Jeffrey, R. 1980
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ROUNDING PERCENTAGES
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
1979; 74 (366): 359-364
View details for Web of Science ID A1979HD79300014
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CONJUGATE PRIORS FOR EXPONENTIAL FAMILIES
ANNALS OF STATISTICS
1979; 7 (2): 269-281
View details for Web of Science ID A1979GU38500003
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SOME TAUBERIAN THEOREMS RELATED TO COIN TOSSING
ANNALS OF PROBABILITY
1978; 6 (3): 483-490
View details for Web of Science ID A1978FE07700010
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STATISTICAL PROBLEMS IN ESP RESEARCH
SCIENCE
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
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EXAMPLES FOR THEORY OF INFINITE ITERATION OF SUMMABILITY METHODS
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
1977; 29 (3): 489-497
View details for Web of Science ID A1977DH79600006
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2ND-ORDER TERMS FOR VARIANCES AND COVARIANCES OF NUMBER OF PRIME FACTORS - INCLUDING SQUARE FREE CASE
JOURNAL OF NUMBER THEORY
1977; 9 (2): 187-202
View details for Web of Science ID A1977DJ18500006
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SPEARMANS FOOTRULE AS A MEASURE OF DISARRAY
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
1977; 39 (2): 262-268
View details for Web of Science ID A1977DY62900010
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FINITE FORMS OF DE FINETTS THEOREM ON EXCHANGEABILITY
SYNTHESE
1977; 36 (2): 271-281
View details for Web of Science ID A1977ED80600004
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DISTRIBUTION OF LEADING DIGITS AND UNIFORM-DISTRIBUTION MOD-1
ANNALS OF PROBABILITY
1977; 5 (1): 72-81
View details for Web of Science ID A1977CV74200005
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BUFFONS PROBLEM WITH A LONG NEEDLE
JOURNAL OF APPLIED PROBABILITY
1976; 13 (3): 614-618
View details for Web of Science ID A1976CH05600022
- Protocol Issues in Randomized Clinical Trials of a Surgical Treatment of Duodenal Ulcer Costs, Risks and Benefits of Surgery edited by Bunker, J., Barnes, B., Mosteller, F. Oxford University Press. 1976