A dozen de Finetti-style results in search of a theory

Persi Diaconis; David Freedman

Annales de l'I.H.P. Probabilités et statistiques (1987)

  • Volume: 23, Issue: S2, page 397-423
  • ISSN: 0246-0203

How to cite


Diaconis, Persi, and Freedman, David. "A dozen de Finetti-style results in search of a theory." Annales de l'I.H.P. Probabilités et statistiques 23.S2 (1987): 397-423. <http://eudml.org/doc/77315>.

author = {Diaconis, Persi, Freedman, David},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {de Finetti's theorem; exchangeable; orthogonally invariant; variation distance; uniqueness of mixtures; historical remarks},
language = {eng},
number = {S2},
pages = {397-423},
publisher = {Gauthier-Villars},
title = {A dozen de Finetti-style results in search of a theory},
url = {http://eudml.org/doc/77315},
volume = {23},
year = {1987},

AU - Diaconis, Persi
AU - Freedman, David
TI - A dozen de Finetti-style results in search of a theory
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1987
PB - Gauthier-Villars
VL - 23
IS - S2
SP - 397
EP - 423
LA - eng
KW - de Finetti's theorem; exchangeable; orthogonally invariant; variation distance; uniqueness of mixtures; historical remarks
UR - http://eudml.org/doc/77315
ER -


  1. D. Aldous, Exchangeability and Related Topics, Springer Lecture Notes in Math., No. 1196, 1985. Zbl0562.60042MR883646
  2. E. Borel, Introduction géométrique à quelques théories physiques, Gauthier-Villars, Paris, 1914. Zbl45.0808.10JFM45.0808.10
  3. P.C. Billingsley, Probability and Measure, Wiley, New York, 1979. Zbl0411.60001MR534323
  4. I. Csiszár, Sanov Property, Generalized I Projections, and a Conditioned Limit Theorem, Ann. Prob., Vol. 12, 1984, p. 768-793. Zbl0544.60011MR744233
  5. B. De Finetti, Funzioni caratteristica di un fenomeno aleatorio, Atti della R. Academia Nazionale dei Lincei Ser 6, Memorie Classe di Scienze Fisiche, Mathematiche e Naturali, Vol. 4, 1931, pp. 251-299. JFM57.0610.01
  6. B. De Finetti, La prévision: ses lois logiques, ses sources subjectives, Ann. Inst. Henri Poincaré, Vol. 7, 1937, pp. 1-66. Zbl0017.07602MR1508036
  7. P. Diaconis, Finite Forms of de Finetti's Theorem on Exchangeability, Synthèse, Vol. 36, 1978, pp. 271-281. Zbl0397.60005MR517222
  8. P. Diaconis, M. Eaton and S. Lauritzen, (1986). Finite de Finetti Theorems, 1986, Unpublished manuscript. Zbl0795.62049
  9. P. Diaconis and B. Efron, Probabilistic-Geometric Theorems Arising from the Analysis of Contingency Tables, Contributions to the Theory and Application of Statistics, A. GELFAND Ed. Academic Press, Boston, pp. 103-125. Zbl0709.60566MR901121
  10. P. Diaconis and D. Freedman, Finite Exchangeable Sequences, Ann. Prob., Vol. 8, 1980, pp. 745-764. Zbl0434.60034MR577313
  11. P. Diaconis and D. Freedman, Partial Exchangeability and Sufficiency, in Statistics, Applications, and New Directions, J. K. GHOSH and J. ROY Eds., 1984, pp. 205-236, Indian Statistical Institute, Calcutta. MR786142
  12. P. Diaconis and D. Freedman, A Finite Version of de Finetti's Theorem for Exponential Families with Uniform Asymptotic Estimates, Technical report, Department of Statistics, University of California, Berkeley, 1986. 
  13. L. Dubins and D. Freedman, Exchangeable Processes Need Not be Mixtures of Independent Identically Distributed Random Variables, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, Vol. 48, 1979, pp. 115-132. Zbl0388.60036MR534840
  14. M. Eaton, On the Projections of Isotropic Distributions, Ann. Stat., 9, 1981, pp. 391-400. Zbl0463.62016MR606622
  15. W. Feller, An Introduction to Probability Theory and Its Applications, Vol. I, 3rd Edition, Wiley, New York, 1968. Zbl0155.23101MR228020
  16. W. Feller, An Introduction to Probability Theory and Its Applications, Vol. II, 2nd Edition, Wiley, New York, 1971. Zbl0219.60003MR270403
  17. D. Freedman, Invariants Under Mixing which Generalize de Finetti's Theorem, Ann. Math. Statist., Vol. 33, 1962, pp. 916-923. Zbl0201.49501MR156369
  18. D. Freedman, Invariants Under Mixing which Generalize de Finetti's Theorem: Coninuous Time Parameter, Ann. Math. Statist., Vol. 34, 1963, pp. 1194-1216. Zbl0253.60064MR189111
  19. D. Freedman and D. Lane, The Empirical Distribution of Fourier Coefficients, Ann. Stat., Vol. 8, 1980, pp. 1244-51. Zbl0449.62036MR594641
  20. L. Gallardo, Au sujet du contenu probabiliste d'un lemma d'Henri Poincaré, Annales de l'Université de Clermont, Vol. 69, 1983, pp. 192-197. 
  21. R. Gâteaux, Sur la notion d'intégrale dans le domaine fonctionnel et sur la théorie du potentiel, Bull. Soc. Math. France, Vol. 47, 1919, pp. 47-67. Zbl47.0382.01JFM47.0382.01
  22. E. Hewitt and L.J. Savage, Symmetric Measures on Cartesian Products, Trans. Amer. Math. Soc., Vol. 80, 1955, pp. 470-501. Zbl0066.29604MR76206
  23. L. Holst, Two Conditional Limit Theorems with Applications, Ann. Prob., Vol. 7, 1979, pp. 1066-1072. MR527490
  24. N. Johnson and N.L. Kotz, Urn Models and their Applications, Wiley, New York, 1977. Zbl0352.60001MR488211
  25. J. Kersten, Verallgemeinerung eines Satzes von Prochrow und LeCam, Zeitschrift für Wahrscheinlichkeistheorie und verwandte Gebiete, Vo. 2, 1963, pp. 173-179. Zbl0123.35403
  26. S.L. Lauritzen, Extreme Point Models in Statistics, Scand. Jour. Statist., Vol. 11, 1984, pp. 65-91. Zbl0542.62002MR754971
  27. L. Lecam, Une théorème sur la division d'un intervalle par des points pris au hasard, Publ. Inst. Statist. Universitaire Paris, Vol. 7, 1958, pp. 7-16. Zbl0083.13803MR105735
  28. G. Letac, Isotropy and Sphericity: Some Characterizations, Ann. Stat., Vol. 9, 1981, pp. 408- 417. Zbl0462.62014MR606624
  29. P. Lévy, Leçons d'Analyse Fonctionnelle, Gauthier-Villars, Paris, 1922. JFM48.0453.01
  30. P. Levy, Analyse Fonctionnelle, Mémorial des Sciences Mathématiques, Vol 5, Gauthier-Villars, Paris, 1925. JFM51.0311.02
  31. P. Lévy, Problèmes concrets d'analyse fonctionnelle, Gauthier-Villars, Paris, 1951. Zbl0043.32302MR41346
  32. P. Martin-Lof, Statistika Modeller Anteckningar fran seminarier läsåret, 1969-70 urarbetade av R. Sunberg, Institutionen för matematisk statistik, Stockholm's universitet. 
  33. J.C. Maxwell, Theory of Heat, 4th ed. Longmans, London, 1875. Zbl1207.80001
  34. J.C. Maxwell, On Boltzmann's theorem on the average distribution of energy in a system of material points, Cambridge Phil. Soc. Trans., Vol. 12, 1878, p. 547. JFM11.0776.01
  35. H. Mckean, Geometry of differential space, Ann. Prob., Vol. 1, 1973, pp. 197-206. Zbl0263.60035MR353471
  36. H. Poincaré, Calcul des probabilités, Gauthier-Villars, Paris, 1912. JFM43.0308.04
  37. R. Pyke, Spacings, J. Royal Statist. Soc., B, Vol. 7, 1965, pp. 395-449. Zbl0144.41704MR216622
  38. P. Ressell, de Finetti Type Theorems: an Analytic Approach, Ann. Prob., Vol. 13, 1985, pp. 898-922. Zbl0579.60012MR799427
  39. D. Ruelle, Thermodynamic Formalism, Addison Wesley, Reading, Mass., 1978. Zbl0401.28016MR511655
  40. I.J. Schoenberg, Metric Spaces and Positive Definite Functions, Trans. Amer. Math. Soc., Vol. 44, 1938, pp. 522-536. Zbl0019.41502MR1501980JFM64.0617.02
  41. A.J. Stam, Limit Theorems for Uniform Distributions on High Dimensional Euclidean Spaces, J. Appl. Prob., Vol. 19, 1982, pp. 221-228. Zbl0485.60024MR644435
  42. V. Vervaat, Upper Bounds for the Distance in Total Variation Between the Binomial or Negative Binomial and the Poisson Distribution, Statistica Neerlandica, Vol. 23, 1970, pp. 79-86. Zbl0162.22203MR242235
  43. M. Yor, Inégalités de martingales continus arrêtés à un temps quelconques I, Springer Lecture Notes in Math., No. 1118, 1985. Zbl0563.60045
  44. S. Zabell, Continuous Versions of Regular Conditional Distributions, Ann. Prob., Vol. 7, 1979, pp. 159-165. Zbl0392.60013MR515823
  45. S. Zabell, Rates of Convergence for Conditional Expectations, Ann. Prob., Vol. 8, 1980, pp. 928-941. Zbl0441.60019MR586777
  46. A. Zaman, A Finite Form of de Finetti's Theorem for Stationary Markov Chains, Ann. Prob., Vol. 14, 1986, pp. 1418-27. Zbl0608.60032MR866363

Citations in EuDML Documents

  1. Mustapha Mourragui, Comportement hydrodynamique et entropie relative des processus de sauts, de naissances et de morts
  2. Mohamed Bouali, Application des théorèmes de Minlos et Poincaré à l’étude asymptotique d’une intégrale orbitale
  3. Peter Harremoës, František Matúš, Bounds on the information divergence for hypergeometric distributions
  4. Assaf Naor, Dan Romik, Projecting the surface measure of the sphere of p n
  5. Michel Ledoux, Inégalités isopérimétriques en analyse et probabilités

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.