Pith. sign in

REVIEW 1 major objections 1 minor 135 references

Ferguson's Dirichlet Process Breakthrough: A Lasting Legacy

T0 review · 1 major / 1 minor · reviewed 2026-06-25 · grok-4.3

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Ferguson's 1973 Dirichlet process supplied the first prior on probability measures that combined large support with analytical tractability.

desk verdict Review recaps standard Dirichlet process constructions but renaming proposal rests on thin historical evidence. read the letter →

arxiv 2606.24519 v1 pith:VRWRVIN2 submitted 2026-06-23 math.ST stat.TH

Antonio Lijoi , Igor Pruenster , Junyi Zhang This is my paper · ORCID
classification math.STstat.TH
keywords DirichletprocessBayesiannonparametricsFergusondeFinettinonparametricpriorsgammapredictivedistributions
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that Ferguson's introduction of the Dirichlet process resolved a long-standing obstacle in Bayesian nonparametrics by meeting two requirements that no earlier construction had satisfied simultaneously. It reviews three constructions traceable to Ferguson's work and shows how each construction supplies a pattern for later generalizations. The authors link this advance directly to the framework de Finetti outlined in the 1930s and argue that the process therefore merits the name Ferguson-Dirichlet process. A sympathetic reader would see the review as establishing both the historical priority of the construction and a practical template for building further nonparametric priors.

What carries the argument

The three complementary constructions of the Dirichlet process (finite-dimensional distributions, normalization of a gamma process, and predictive distributions), each serving as a template for further classes of priors.

What would settle it

A documented construction, predating 1973, of a prior on probability measures that already possessed both large support and analytical tractability would falsify the breakthrough claim.

Watch

Extended reading notes

Core claim

Ferguson's 1973 paper introduced the Dirichlet process as a prior on the space of probability measures that for the first time satisfied both large support and analytical tractability, thereby supplying the missing tractable nonparametric prior in the Bayesian framework that de Finetti had set out decades earlier; the authors therefore propose that the process be called the Ferguson-Dirichlet process.

Load-bearing premise

No prior on probability measures with both large support and analytical tractability existed before Ferguson's 1973 construction.

Editorial extensions

If this is right

  • The three constructions supply reusable templates for normalized random measures with independent increments and for Gibbs-type priors.
  • The Dirichlet process has served as the central building block for Bayesian nonparametric methods and their applications.
  • The same ideas have driven the development of a wider collection of nonparametric priors over the subsequent fifty years.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Adopting the Ferguson-Dirichlet name would make historical priority visible in citations and textbooks without changing the mathematics.
  • Parallel historical reviews of other priors could identify additional cases where renaming would clarify credit.
  • The predictive-distribution construction may lend itself to direct extensions that incorporate dependence or covariate information.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 1 minor

Summary. The manuscript reviews Ferguson's 1973 introduction of the Dirichlet process, presenting three constructions (finite-dimensional distributions, gamma process normalization, and predictive distributions) and their role as templates for generalizations such as normalized random measures and Gibbs-type priors. It claims this work solved a decades-long open problem in Bayesian nonparametrics originating with de Finetti in the 1930s, and proposes renaming the Dirichlet process the Ferguson--Dirichlet process.

Significance. As a review paper the manuscript could provide a compact synthesis of constructions if the historical framing is documented; the technical content on constructions and generalizations is standard and does not introduce new results.

major comments (1)
  1. [Abstract and historical narrative] Abstract and opening historical narrative: the assertion that de Finetti 'laid out the Bayesian nonparametric framework in the 1930s' with the 'key obstacle' being 'the absence of a tractable nonparametric prior' is advanced without any citation, quotation, or reference to de Finetti's 1930s publications. This unattributed premise directly supports both the 'breakthrough' designation and the proposed renaming, so explicit documentary evidence is required.
minor comments (1)
  1. Ensure that each of the three constructions is accompanied by precise references to the original Ferguson papers and to subsequent generalizations (e.g., normalized random measures with independent increments).

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment on the historical framing. We address it directly below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: Abstract and opening historical narrative: the assertion that de Finetti 'laid out the Bayesian nonparametric framework in the 1930s' with the 'key obstacle' being 'the absence of a tractable nonparametric prior' is advanced without any citation, quotation, or reference to de Finetti's 1930s publications. This unattributed premise directly supports both the 'breakthrough' designation and the proposed renaming, so explicit documentary evidence is required.

    Authors: We agree that the original text lacked explicit citations for the historical premise. In revision we will insert references to de Finetti (1937) 'La prévision: ses lois logiques, ses sources subjectives' (which develops subjective probability and the representation of exchangeable sequences) together with the 1938 follow-up on exchangeability. These works supply the foundational representation theorem that later enabled Bayesian nonparametric constructions; we will quote or paraphrase the relevant passages on mixtures of i.i.d. processes. The phrase 'key obstacle' is an interpretive gloss on the subsequent literature (post-1930s) that identified the practical need for tractable priors on infinite-dimensional spaces; we will qualify the sentence to make this distinction clear while retaining the link to Ferguson's solution. The added citations and slight rephrasing will appear in both the abstract and the opening paragraph. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: historical review with no self-referential derivations or fitted predictions

full rationale

The paper reviews three constructions of the Dirichlet process (finite-dimensional distributions, gamma process normalization, predictive distributions) and offers a historical narrative on de Finetti and Ferguson. No equations, parameters, or predictions appear that reduce to the paper's own inputs by construction. The renaming proposal rests on the stated historical premise rather than any self-citation chain, self-definition, or ansatz smuggling. The central claim is documentary/historical rather than a derived result, so none of the enumerated circularity patterns apply.

Assumptions & free parameters 0 free parameters · 0 assumptions · 0 invented entities

The paper is a historical review and does not introduce or rely on new free parameters, axioms, or invented entities beyond standard concepts in Bayesian statistics.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Ferguson's Dirichlet Process Breakthrough: A Lasting Legacy." pith.science (2026). https://pith.science/paper/VRWRVIN2

@misc{pith2026260624519,
  author       = {Pith},
  title        = {Pith review of: Ferguson's Dirichlet Process Breakthrough: A Lasting Legacy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VRWRVIN2}},
  note         = {Machine review of arXiv:2606.24519}
}
read the original abstract

Ferguson's 1973 introduction of the Dirichlet process marked a breakthrough in Bayesian nonparametric statistics. For the first time, a prior on the space of probability measures fulfilled two key desiderata: large support and analytical tractability. In this paper, we review three complementary constructions of the Dirichlet process, whose roots can be traced back to Ferguson: through finite-dimensional distributions, via normalization of a gamma process, and through predictive distributions. Each perspective not only deepens the understanding of the Dirichlet process but also provides a template for generalizations, from normalized random measures with independent increments to Gibbs--type priors and beyond. Over the past fifty years, the Dirichlet process has become the cornerstone of Bayesian nonparametric methodology and applications, while simultaneously inspiring the expansion of the landscape of nonparametric priors. Since de Finetti laid out the Bayesian nonparametric framework in the 1930s, the key obstacle had been the absence of a tractable nonparametric prior. Ferguson's contribution overcame this challenge, providing a solution to a decades-long open problem. In recognition of this decisive advance, it seems appropriate to refer to the Dirichlet process as the Ferguson--Dirichlet process.

Figures

Figures reproduced from arXiv: 2606.24519 by the authors.

Figure 1
Figure 1. Beta densities on (0, 1) with the parameters (αi , αi). Dir(.6, .6) ; Dir(.8, .8) ; Dir(1, 1) ; Dir(2, 2) ; Dir(10, 10) ∗ . (a) Dirichlet(.6, .6, .6). (b) Dirichlet(.8, .8, .8). (c) Dirichlet(1, 1, 1). (d) Dirichlet(2, 2, 2) [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Heatmaps for the Dirichlet density on ∆2 corresponding to various parameter settings. 7 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Normalized inverse Gaussian densities on (0 [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Heatmaps for the normalized inverse Gaussian dens [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

135 extracted references · 1 canonical work pages

  1. [1]

    MacEachern , title =

    Steven N. MacEachern , title =. Bayesian Analysis , publisher =

  2. [2]

    and Lijoi, A

    Favaro, S. and Lijoi, A. and Pr\"unster, I. , TITLE =. Biometrika , FJOURNAL =. 2012 , NUMBER =

    2012

  3. [3]

    and Pitman, J

    Perman, M. and Pitman, J. and Yor, M. , title =. Probab

  4. [4]

    and Lijoi, A

    Favaro, S. and Lijoi, A. and Nava, C. and Nipoti, B. and Pr\"unster, I. and Teh, Y. W. , title =. 2016 , publisher =

    2016

  5. [5]

    The Annals of Statistics , number =

    Mar. The Annals of Statistics , number =

  6. [6]

    Fortini, Sandra and Ladelli, Lucia and Regazzini, Eugenio , TITLE =. Sankhy. 2000 , NUMBER =

    2000

  7. [7]

    MacEachern and Peter M\"uller , title =

    Steven N. MacEachern and Peter M\"uller , title =. Journal of Computational and Graphical Statistics , volume =. 1998 , publisher =

    1998

  8. [8]

    Walker , title =

    Stephen G. Walker , title =. Communications in Statistics - Simulation and Computation , volume =. 2007 , publisher =

    2007

Show all 135 references
  1. [9]

    Neal , title =

    Radford M. Neal , title =. Journal of Computational and Graphical Statistics , volume =. 2000 , publisher =

    2000

  2. [10]

    2007 , author =

    Tempering stable processes , journal =. 2007 , author =

    2007

  3. [11]

    De Blasi, Pierpaolo and Lijoi, Antonio and Pr\"unster, Igor , TITLE =. Statist. Sinica , FJOURNAL =. 2013 , NUMBER =

    2013

  4. [12]

    , TITLE =

    Lijoi, Antonio and Pr\"unster, Igor and Walker, Stephen G. , TITLE =. Statist. Sinica , FJOURNAL =. 2008 , NUMBER =

    2008

  5. [13]

    2011 , author =

    On a class of distributions on the simplex , journal =. 2011 , author =

    2011

  6. [14]

    1996 , PAGES =

    Bertoin, Jean , TITLE =. 1996 , PAGES =

    1996

  7. [15]

    Carlton , journal =

    Matthew A. Carlton , journal =. A Family of Densities Derived from the Three-Parameter Dirichlet Process , volume =

  8. [16]

    and Pr\"unster, Igor , title =

    Lijoi, Antonio and Mena, Ramsés H. and Pr\"unster, Igor , title =. Biometrika , volume =. 2007 , month =

    2007

  9. [17]

    and Pr\"unster, Igor , TITLE =

    Lijoi, Antonio and Mena, Rams\'es H. and Pr\"unster, Igor , TITLE =. Stat. Inference Stoch. Process. , FJOURNAL =. 2005 , NUMBER =

    2005

  10. [18]

    Rendiconti del Circolo Matematico di Palermo , volume=

    Sulle funzioni ipergeometriche a piu variabili , author=. Rendiconti del Circolo Matematico di Palermo , volume=. 1893 , publisher=

  11. [19]

    and Savage, I

    Berk, Robert H. and Savage, I. Richard , TITLE =. Contributions to statistics , PAGES =

  12. [20]

    Impostazione non parametrica di problemi d'inferenza statistica bayesiana , journal=

    Regazzini, Eugenio , year=. Impostazione non parametrica di problemi d'inferenza statistica bayesiana , journal=

  13. [21]

    Il problema della perequazione , journal=

    de Finetti, Bruno , year=. Il problema della perequazione , journal=

  14. [22]

    , TITLE =

    Blackwell, David and MacQueen, James B. , TITLE =. Ann. Statist. , FJOURNAL =. 1973 , PAGES =

    1973

  15. [23]

    and Pr\"unster, Igor , TITLE =

    Barrios, Ernesto and Lijoi, Antonio and Nieto-Barajas, Luis E. and Pr\"unster, Igor , TITLE =. Statist. Sci. , FJOURNAL =. 2013 , NUMBER =

    2013

  16. [24]

    Escobar, Micheal D and West, Mike , journal =

  17. [25]

    Antoniak , date-modified =

    Charles E. Antoniak , date-modified =. The Annals of Statistics , number =. 1974 , MRNUMBER =

    1974

  18. [26]

    Daley, D. J. and Vere-Jones, D. , TITLE =. 2008 , PAGES =

    2008

  19. [27]

    Ewens , date-modified =

    W.J. Ewens , date-modified =. The sampling theory of selectively neutral alleles , volume =. Theoretical Population Biology , number =

  20. [28]

    The ubiquitous

    Crane, Harry , journal=. The ubiquitous

  21. [29]

    Tavar\'e, Simon , title =. Bull. Lond. Math. Soc. , volume =

  22. [30]

    Quintana, Fernando A. and M\". The dependent. Statist. Sci. , number =

  23. [31]

    Korwar and Myles Hollander , journal =

    Ramesh M. Korwar and Myles Hollander , journal =. Contributions to the Theory of Dirichlet Processes , volume =

  24. [32]

    Intorno ad alcune questioni relative alla definizione del premio secondo la teoria della credibilit

    Eugenio Regazzini , journal =. Intorno ad alcune questioni relative alla definizione del premio secondo la teoria della credibilit

  25. [33]

    Denti, Francesco and Camerlenghi, Federico and Guindani, Michele and Mira, Antonietta , TITLE =. J. Amer. Statist. Assoc. , FJOURNAL =. 2023 , NUMBER =

    2023

  26. [34]

    Bayesian nonparametric estimation based on censored data , author=. Ann. Stat. , volume =

  27. [35]

    2025 , journal=

    Multivariate Species Sampling Models , author=. 2025 , journal=. 2503.24004 , archivePrefix=

    2025

  28. [36]

    Wade, Sara and In\'acio, Vanda , TITLE =. Statist. Sci. , FJOURNAL =. 2025 , NUMBER =

    2025

  29. [37]

    Hjort, Nils Lid , TITLE =. Ann. Statist. , FJOURNAL =. 1990 , NUMBER =

    1990

  30. [38]

    , TITLE =

    Kraft, Charles H. , TITLE =. J. Appl. Probability , FJOURNAL =. 1964 , PAGES =

    1964

  31. [39]

    and van Eeden, Constance , TITLE =

    Kraft, Charles H. and van Eeden, Constance , TITLE =. Ann. Math. Statist. , FJOURNAL =. 1964 , PAGES =

    1964

  32. [40]

    and Freedman, David A

    Dubins, Lester E. and Freedman, David A. , TITLE =. Proc. 1967 , MRCLASS =

    1967

  33. [41]

    , TITLE =

    Freedman, David A. , TITLE =. Ann. Math. Statist. , FJOURNAL =. 1963 , PAGES =

    1963

  34. [42]

    Lavine, Michael , TITLE =. Ann. Statist. , FJOURNAL =. 1992 , NUMBER =

    1992

  35. [43]

    Daniel and Sudderth, William D

    Mauldin, R. Daniel and Sudderth, William D. and Williams, S. C. , TITLE =. Ann. Statist. , FJOURNAL =. 1992 , NUMBER =

    1992

  36. [44]

    , TITLE =

    Fabius, J. , TITLE =. Ann. Math. Statist. , FJOURNAL =. 1964 , PAGES =

    1964

  37. [45]

    , TITLE =

    Sethuraman, Jayaram and Tiwari, Ram C. , TITLE =. Statistical decision theory and related topics,. 1982 , MRCLASS =

    1982

  38. [46]

    Combinatorial Stochastic Processes , year =

    Jim Pitman , publisher =. Combinatorial Stochastic Processes , year =

  39. [47]

    Blackwell, David , TITLE =. Ann. Statist. , FJOURNAL =. 1973 , PAGES =

    1973

  40. [48]

    2017 , PAGES =

    Ghosal, Subhashis and van der Vaart, Aad , TITLE =. 2017 , PAGES =

    2017

  41. [49]

    2015 , PAGES =

    M\"uller, Peter and Quintana, Fernando Andr\'es and Jara, Alejandro and Hanson, Tim , TITLE =. 2015 , PAGES =

    2015

  42. [50]

    2010 , PAGES =

    Bayesian nonparametrics , SERIES =. 2010 , PAGES =

    2010

  43. [51]

    S. R. Dalal and Gaineford J. Hall , title =. The Annals of Statistics , number =

  44. [52]

    , title =

    Lo, Albert Y. , title =. Annals of Statistics , volume =. 1984 , publisher =

    1984

  45. [53]

    , TITLE =

    Ferguson, Thomas S. , TITLE =. Recent advances in statistics , PAGES =. 1983 , MRCLASS =

    1983

  46. [54]

    Statistics & Probability Letters , volume =

    Majumdar, Suman , title =. Statistics & Probability Letters , volume =

  47. [55]

    Doksum , title =

    Kjell A. Doksum , title =. Annals of Probability , volume =. 1974 , publisher =

    1974

  48. [56]

    Savage , title =

    Edwin Hewitt and Leonard J. Savage , title =. Transactions of the American Mathematical Society , volume =

  49. [57]

    2018 , publisher =

    Persi Diaconis and Brian Skyrms , title =. 2018 , publisher =

    2018

  50. [58]

    1739 , publisher =

    David Hume , title =. 1739 , publisher =

  51. [59]

    Lindley, D. V. , TITLE =. 1972 , PAGES =

    1972

  52. [60]

    Flexible clustering via hidden hierarchical

    Lijoi, Antonio and Pr\". Flexible clustering via hidden hierarchical. Scand. J. Stat. , FJOURNAL =. 2023 , NUMBER =

    2023

  53. [61]

    and Lijoi, Antonio and Pr\"

    Camerlenghi, Federico and Dunson, David B. and Lijoi, Antonio and Pr\". Latent nested nonparametric priors (with discussion) , NOTE =. Bayesian Anal. , FJOURNAL =. 2019 , NUMBER =

    2019

  54. [62]

    Camerlenghi, Federico and Lijoi, Antonio and Pr\"unster, Igor , TITLE =. Scand. J. Stat. , FJOURNAL =. 2018 , NUMBER =

    2018

  55. [63]

    The nested

    Rodr\'. The nested. J. Amer. Statist. Assoc. , FJOURNAL =. 2008 , NUMBER =

    2008

  56. [64]

    2025 , journal=

    Hierarchical random measures without tables , author=. 2025 , journal=

    2025

  57. [65]

    Bayesian Analysis , publisher =

    Marta Catalano and Claudio Del Sole , title =. Bayesian Analysis , publisher =

  58. [66]

    2025 , journal=

    Measures of Dependence based on Wasserstein distances , author=. 2025 , journal=

    2025

  59. [67]

    A unified approach to hierarchical random measures , JOURNAL =

    Catalano, Marta and Del Sole, Claudio and Lijoi, Antonio and Pr\". A unified approach to hierarchical random measures , JOURNAL =. 2024 , NUMBER =

    2024

  60. [68]

    Catalano, Marta and Lijoi, Antonio and Pr\"unster, Igor , TITLE =. Ann. Statist. , FJOURNAL =. 2021 , NUMBER =

    2021

  61. [69]

    Journal of the American Statistical Association , volume =

    Marta Catalano and Hugo Lavenant and Antonio Lijoi and Igor Pr\"unster , title =. Journal of the American Statistical Association , volume =. 2024 , publisher =

    2024

  62. [70]

    2025 , journal=

    Measuring partial exchangeability with Reproducing Kernel Hilbert Spaces , author=. 2025 , journal=

    2025

  63. [71]

    , author=

    Problemi statistici non parametrici in condizioni di scambiabilit\`a parziale e impiego di medie associative. , author=. 1978 , institution=

    1978

  64. [72]

    Survival analysis via hierarchically dependent mixture hazards , JOURNAL =

    Camerlenghi, Federico and Lijoi, Antonio and Pr\". Survival analysis via hierarchically dependent mixture hazards , JOURNAL =. 2021 , NUMBER =

    2021

  65. [73]

    Distribution theory for hierarchical processes , JOURNAL =

    Camerlenghi, Federico and Lijoi, Antonio and Orbanz, Peter and Pr\". Distribution theory for hierarchical processes , JOURNAL =. 2019 , NUMBER =

    2019

  66. [74]

    Dependent mixture models: clustering and borrowing information , JOURNAL =

    Lijoi, Antonio and Nipoti, Bernardo and Pr\". Dependent mixture models: clustering and borrowing information , JOURNAL =. 2014 , PAGES =

    2014

  67. [75]

    Bayesian inference with dependent normalized completely random measures , JOURNAL =

    Lijoi, Antonio and Nipoti, Bernardo and Pr\". Bayesian inference with dependent normalized completely random measures , JOURNAL =. 2014 , NUMBER =

    2014

  68. [76]

    A method for combining inference across related nonparametric

    M\". A method for combining inference across related nonparametric. J. R. Stat. Soc. Ser. B Stat. Methodol. , FJOURNAL =. 2004 , NUMBER =

    2004

  69. [77]

    Dependent

    MacEachern, Steven N , journal=. Dependent

  70. [78]

    ASA proceedings of the section on Bayesian statistical science , volume=

    Dependent nonparametric processes , author=. ASA proceedings of the section on Bayesian statistical science , volume=. 1999 , organization=

    1999

  71. [79]

    1938 , journal=

    Sur la condition d'\'equivalence partielle , author=. 1938 , journal=

    1938

  72. [80]

    Electron

    Dassios, Angelos and Zhang, Junyi , TITLE =. Electron. J. Probab. , FJOURNAL =. 2021 , PAGES =

    2021

  73. [81]

    Zhang, Junyi and Dassios, Angelos , TITLE =. Scand. J. Stat. , FJOURNAL =. 2024 , NUMBER =

    2024

  74. [82]

    Zhang, Junyi and Dassios, Angelos , TITLE =. Stat. Comput. , FJOURNAL =. 2023 , NUMBER =

    2023

  75. [83]

    , TITLE =

    Wilks, Samuel S. , TITLE =. 1962 , PAGES =

    1962

  76. [84]

    Journal of the Itailan Statistical Society , YEAR =

    Regazzini, Eugenio and Petris, Giovanni , TITLE =. Journal of the Itailan Statistical Society , YEAR =

  77. [85]

    International statistical review , volume=

    Exchangeability, correlation, and Bayes' effect , author=. International statistical review , volume=. 2009 , publisher=

    2009

  78. [86]

    Philosophy and Phenomenological Research , volume=

    The uniformity of nature , author=. Philosophy and Phenomenological Research , volume=. 1953 , publisher=

    1953

  79. [87]

    Bayesian Analysis , volume=

    Posterior Sampling From Truncated Ferguson-Klass Representation of Normalised Completely Random Measure Mixtures , author=. Bayesian Analysis , volume=. 2024 , publisher=

    2024

  80. [88]

    Artificial Intelligence and Statistics , year=

    Zhang, Junyi and Dassios, Angelos and Zhong, Chong and Yao, Qiufei , TITLE =. Artificial Intelligence and Statistics , year=

  81. [89]

    , TITLE =

    Kyprianou, Andreas E. , TITLE =. 2006 , PAGES =

    2006

  82. [90]

    , TITLE =

    James, Lancelot F. , TITLE =. Ann. Statist. , FJOURNAL =. 2006 , NUMBER =

    2006

  83. [91]

    L\'evy processes , PAGES =

    Rosi\'nski, Jan , TITLE =. L\'evy processes , PAGES =. 2001 , MRCLASS =

    2001

  84. [92]

    Kingman, J.F.C , TITLE =. J. Roy. Statist. Soc. Ser. B , FJOURNAL =. 1975 , PAGES =

    1975

  85. [93]

    and Pr\"unster, Igor , TITLE =

    Lijoi, Antonio and Mena, Rams\'es H. and Pr\"unster, Igor , TITLE =. J. R. Stat. Soc. Ser. B Stat. Methodol. , FJOURNAL =. 2007 , NUMBER =

    2007

  86. [94]

    Kingman, J. F. C. , TITLE =. 1993 , PAGES =

    1993

  87. [95]

    Kingman, J. F. C. , TITLE =. Pacific J. Math. , FJOURNAL =. 1967 , PAGES =

    1967

  88. [96]

    and Pr\"unster, Igor , TITLE =

    Lijoi, Antonio and Mena, Rams\'es H. and Pr\"unster, Igor , TITLE =. J. Amer. Statist. Assoc. , FJOURNAL =. 2005 , NUMBER =

    2005

  89. [97]

    Lindley, D. V. and Smith, A. F. M. , TITLE =. J. Roy. Statist. Soc. Ser. B , FJOURNAL =. 1972 , PAGES =

    1972

  90. [98]

    Pitman, Jim and Yor, Marc , TITLE =. Ann. Probab. , FJOURNAL =. 1997 , NUMBER =

    1997

  91. [99]

    and Pitman, J

    Gnedin, A. and Pitman, J. , TITLE =. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) , FJOURNAL =. 2005 , PAGES =

    2005

  92. [100]

    Sethuraman, Jayaram , TITLE =. Statist. Sinica , FJOURNAL =. 1994 , NUMBER =

    1994

  93. [101]

    IEEE transactions on pattern analysis and machine intelligence , volume=

    Are Gibbs-type priors the most natural generalization of the Dirichlet process? , author=. IEEE transactions on pattern analysis and machine intelligence , volume=. 2015 , publisher=

    2015

  94. [102]

    and Hollander, Myles , TITLE =

    Korwar, Ramesh M. and Hollander, Myles , TITLE =. Ann. Probability , FJOURNAL =. 1973 , PAGES =

    1973

  95. [103]

    , TITLE =

    Lo, Albert Y. , TITLE =. Statist. Probab. Lett. , FJOURNAL =. 1991 , NUMBER =

    1991

  96. [104]

    Annali del’Instituto di Matematica Finianziara dell’Universita di Torino, Serie , volume=

    Nonparametric statistical problems under partial exchangeability: The use of associative means , author=. Annali del’Instituto di Matematica Finianziara dell’Universita di Torino, Serie , volume=

  97. [105]

    and Lijoi, Antonio and Pr\"unster, Igor , TITLE =

    James, Lancelot F. and Lijoi, Antonio and Pr\"unster, Igor , TITLE =. Scand. J. Statist. , FJOURNAL =. 2006 , NUMBER =

    2006

  98. [106]

    Biometrika , FJOURNAL =

    Walker, Stephen and Damien, Paul , TITLE =. Biometrika , FJOURNAL =. 2000 , NUMBER =

    2000

  99. [107]

    and Klass, Michael J

    Ferguson, Thomas S. and Klass, Michael J. , TITLE =. Ann. Math. Statist. , FJOURNAL =. 1972 , PAGES =

    1972

  100. [108]

    Statistics, probability and game theory , SERIES =

    Pitman, Jim , TITLE =. Statistics, probability and game theory , SERIES =. 1996 , MRCLASS =

    1996

  101. [109]

    La pr\'evision: ses lois logiques, ses sources subjectives , volume =

    de Finetti, Bruno , journal =. La pr\'evision: ses lois logiques, ses sources subjectives , volume =

  102. [110]

    Dykstra, R. L. and Laud, Purushottam , TITLE =. Ann. Statist. , FJOURNAL =. 1981 , NUMBER =

    1981

  103. [111]

    Brix, Anders , TITLE =. Adv. in Appl. Probab. , FJOURNAL =. 1999 , NUMBER =

    1999

  104. [112]

    Ghosh, J. K. and Ramamoorthi, R. V. , TITLE =. 2003 , PAGES =

    2003

  105. [113]

    Regazzini, Eugenio and Lijoi, Antonio and Pr\"unster, Igor , TITLE =. Ann. Statist. , FJOURNAL =. 2003 , NUMBER =

    2003

  106. [114]

    Bayesian nonparametrics , SERIES =

    Lijoi, Antonio and Pr\"unster, Igor , TITLE =. Bayesian nonparametrics , SERIES =. 2010 , MRCLASS =

    2010

  107. [115]

    and Lijoi, Antonio and Pr\"unster, Igor , TITLE =

    James, Lancelot F. and Lijoi, Antonio and Pr\"unster, Igor , TITLE =. Scand. J. Stat. , FJOURNAL =. 2009 , NUMBER =

    2009

  108. [116]

    , TITLE =

    Ferguson, Thomas S. , TITLE =. Ann. Statist. , FJOURNAL =. 1973 , PAGES =

    1973

  109. [117]

    and Ma, Li , TITLE =

    Wong, Wing H. and Ma, Li , TITLE =. Ann. Statist. , FJOURNAL =. 2010 , NUMBER =

    2010

  110. [118]

    Christensen, Jonathan and Ma, Li , TITLE =. J. R. Stat. Soc. Ser. B. Stat. Methodol. , FJOURNAL =. 2020 , NUMBER =

    2020

  111. [119]

    , TITLE =

    Ferguson, Thomas S. , TITLE =. Ann. Statist. , FJOURNAL =. 1974 , PAGES =

    1974

  112. [120]

    and Van Ryzin, J

    Susarla, V. and Van Ryzin, J. , TITLE =. J. Amer. Statist. Assoc. , FJOURNAL =. 1976 , NUMBER =

    1976

  113. [121]

    and Ramamoorthi, R.V

    Dey, Jyotirmoy and Erickson, R.V. and Ramamoorthi, R.V. , TITLE =. International Statistical Review , VOLUME =. 2003 , NUMBER =

    2003

  114. [122]

    , TITLE =

    Ishwaran, Hemant and James, Lancelot F. , TITLE =. J. Amer. Statist. Assoc. , FJOURNAL =. 2001 , NUMBER =

    2001

  115. [123]

    and Park, Ju-Hyun , title =

    Dunson, David B. and Park, Ju-Hyun , title =. Biometrika , volume =. 2008 , month =

    2008

  116. [124]

    Bayesian Analysis , number =

    Akira Horiguchi and Cliburn Chan and Li Ma , title =. Bayesian Analysis , number =

  117. [125]

    and Mena, Rams\'es H

    Gil-Leyva, Mar\'ia F. and Mena, Rams\'es H. , TITLE =. J. Amer. Statist. Assoc. , FJOURNAL =. 2023 , NUMBER =

    2023

  118. [126]

    and Savage, I

    Berk, Robert H. and Savage, I. Richard , TITLE =. Contributions to statistics , PAGES =. 1979 , MRCLASS =

    1979

  119. [127]

    Journal of the Royal Statistical Society Series B: Statistical Methodology , volume =

    Todeschini, Adrien and Miscouridou, Xenia and Caron, François , title =. Journal of the Royal Statistical Society Series B: Statistical Methodology , volume =. 2020 , month =

    2020

  120. [128]

    Teh, Yee Whye and Jordan, Michael I. , year=. Hierarchical Bayesian nonparametric models with applications , booktitle=

  121. [129]

    Proceedings of the 21st International Conference on Computational Linguistics and 44th Annual Meeting of the Association for Computational Linguistics , pages=

    A hierarchical Bayesian language model based on Pitman-Yor processes , author=. Proceedings of the 21st International Conference on Computational Linguistics and 44th Annual Meeting of the Association for Computational Linguistics , pages=

  122. [130]

    and Ruggiero, Matteo and Span\`o, Dario , TITLE =

    Costantini, Cristina and De Blasi, Pierpaolo and Ethier, Stewart N. and Ruggiero, Matteo and Span\`o, Dario , TITLE =. Ann. Appl. Probab. , FJOURNAL =. 2017 , NUMBER =

    2017

  123. [131]

    2010 , PAGES =

    Feng, Shui , TITLE =. 2010 , PAGES =

    2010

  124. [132]

    and Pr\"unster, Igor , title =

    Favaro, Stefano and Lijoi, Antonio and Mena, Ramsés H. and Pr\"unster, Igor , title =. Journal of the Royal Statistical Society Series B: Statistical Methodology , volume =. 2009 , month =

    2009

  125. [133]

    , title =

    Caron, François and Fox, Emily B. , title =. Journal of the Royal Statistical Society Series B: Statistical Methodology , volume =. 2017 , month =

    2017

  126. [134]

    and Beal, Matthew J

    Teh, Yee Whye and Jordan, Michael I. and Beal, Matthew J. and Blei, David M. , TITLE =. J. Amer. Statist. Assoc. , FJOURNAL =. 2006 , NUMBER =

    2006

  127. [135]

    Proceedings of

    Devroye, Luc , TITLE =. Proceedings of. 2010 , MRCLASS =

    2010

Pith tools

Reviewed June 25, 2026 · model on record in the stance chip above.