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  • Arratia, Richard; Barbour, A. D.; Tavaré, Simon. Logarithmic combinatorial structures: a probabilistic approach. EMS Monographs in Mathematics. European Mathematical Society (EMS), Zurich, 2003. xii+363 pp. ISBN: 3-03719-000-0 MR2032426
  • Bacallado, Sergio; Favaro, Stefano; and Trippa, Lorenzo (2013). Looking-backward probabilities for Gibbs-type exchangeable random partitions. Bernoulli, to appear.
  • Charalambides, Charalambos A. Combinatorial methods in discrete distributions. Wiley Series in Probability and Statistics. Wiley-Interscience [John Wiley & Sons], Hoboken, NJ, 2005. xiv+415 pp. ISBN: 0-471-68027-3 MR2131068
  • Dembo, Amir; Zeitouni, Ofer. Large deviations techniques and applications. Second edition. Applications of Mathematics (New York), 38. Springer-Verlag, New York, 1998. xvi+396 pp. ISBN: 0-387-98406-2 MR1619036
  • Ewens, W. J. The sampling theory of selectively neutral alleles. Theoret. Population Biology 3 (1972), 87--112; erratum, ibid. 3 (1972), 240; erratum, ibid. 3 (1972), 376. MR0325177
  • Favaro, Stefano; Lijoi, Antonio; Mena, Ramsés H.; Pruenster, Igor. Bayesian non-parametric inference for species variety with a two-parameter Poisson-Dirichlet process prior. J. R. Stat. Soc. Ser. B Stat. Methodol. 71 (2009), no. 5, 993--1008. MR2750254
  • Favaro, Stefano; Lijoi, Antonio; Pruenster, Igor. Conditional formulae for Gibbs-type exchangeable random partitions. Ann. Appl. Probab. 23 (2013), no. 5, 1721--1754. MR3114915
  • Feng, Shui. Large deviations associated with Poisson-Dirichlet distribution and Ewens sampling formula. Ann. Appl. Probab. 17 (2007), no. 5-6, 1570--1595. MR2358634
  • Feng, Shui. The Poisson-Dirichlet distribution and related topics. Models and asymptotic behaviors. Probability and its Applications (New York). Springer, Heidelberg, 2010. xiv+218 pp. ISBN: 978-3-642-11193-8 MR2663265
  • Feng, Shui; Hoppe, Fred M. Large deviation principles for some random combinatorial structures in population genetics and Brownian motion. Ann. Appl. Probab. 8 (1998), no. 4, 975--994. MR1661315
  • Ferguson, Thomas S. A Bayesian analysis of some nonparametric problems. Ann. Statist. 1 (1973), 209--230. MR0350949
  • Flajolet, Philippe; Dumas, Philippe; Puyhaubert, Vincent. Some exactly solvable models of urn process theory. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 59--118, Discrete Math. Theor. Comput. Sci. Proc., AG, Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2006. MR2509623
  • Gnedin, A.; Pitman, J. Exchangeable Gibbs partitions and Stirling triangles. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 325 (2005), Teor. Predst. Din. Sist. Komb. i Algoritm. Metody. 12, 83--102, 244--245; translation in J. Math. Sci. (N. Y.) 138 (2006), no. 3, 5674--5685 MR2160320
  • Griffiths, Robert C.; Spanò, Dario. Record indices and age-ordered frequencies in exchangeable Gibbs partitions. Electron. J. Probab. 12 (2007), 1101--1130. MR2336601
  • Hoppe, Fred M. Pòlya-like urns and the Ewens' sampling formula. J. Math. Biol. 20 (1984), no. 1, 91--94. MR0758915
  • Janson, Svante. Limit theorems for triangular urn schemes. Probab. Theory Related Fields 134 (2006), no. 3, 417--452. MR2226887
  • Korwar, Ramesh M.; Hollander, Myles. Contributions to the theory of Dirichlet processes. Ann. Probability 1 (1973), 705--711. MR0350950
  • Lijoi, Antonio; Mena, Ramsés H.; Pruenster, Igor. Bayesian nonparametric estimation of the probability of discovering new species. Biometrika 94 (2007), no. 4, 769--786. MR2416792
  • Lijoi, Antonio; Pruenster, Igor; Walker, Stephen G. Bayesian nonparametric estimators derived from conditional Gibbs structures. Ann. Appl. Probab. 18 (2008), no. 4, 1519--1547. MR2434179
  • Perman, Mihael; Pitman, Jim; Yor, Marc. Size-biased sampling of Poisson point processes and excursions. Probab. Theory Related Fields 92 (1992), no. 1, 21--39. MR1156448
  • Pitman, Jim. Exchangeable and partially exchangeable random partitions. Probab. Theory Related Fields 102 (1995), no. 2, 145--158. MR1337249
  • Pitman, Jim. Partition structures derived from Brownian motion and stable subordinators. Bernoulli 3 (1997), no. 1, 79--96. MR1466546
  • Pitman, Jim; Yor, Marc. The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Ann. Probab. 25 (1997), no. 2, 855--900. MR1434129
  • Pitman, Jim. Poisson-Kingman partitions. Statistics and science: a Festschrift for Terry Speed, 1--34, IMS Lecture Notes Monogr. Ser., 40, Inst. Math. Statist., Beachwood, OH, 2003. MR2004330
  • Pitman, J. Combinatorial stochastic processes. Lectures from the 32nd Summer School on Probability Theory held in Saint-Flour, July 7–24, 2002. With a foreword by Jean Picard. Lecture Notes in Mathematics, 1875. Springer-Verlag, Berlin, 2006. x+256 pp. ISBN: 978-3-540-30990-1; 3-540-30990-X MR2245368
  • Tavaré, Simon. The birth process with immigration, and the genealogical structure of large populations. J. Math. Biol. 25 (1987), no. 2, 161--168. MR0896431
  • Zabell, S.L. (1997). The continuum of inductive methods revisited. In The cosmos of science: essays of exploration, Earman, J. and Norton, J.D. University of Pittsburgh Press.

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