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A family of densities derived from the three-parameter Dirichlet process

Part of: Stochastic processes Distribution theory

Published online by Cambridge University Press:  14 July 2016

Matthew A. Carlton
Matthew A. Carlton*
Affiliation:
California Polytechnic State University
*
∗ Postal address: Department of Statistics, California Polytechnic State University, San Luis Obispo, CA 93407, USA. Email address: mcarlton@calpoly.edu
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Abstract

The traditional Dirichlet process is characterized by its distribution on a measurable partition of the state space - namely, the Dirichlet distribution. In this paper, we consider a generalization of the Dirichlet process and the family of multivariate distributions it induces, with particular attention to a special case where the multivariate density function is tractable.

Keywords

Dirichlet processrandom measuredensity function

MSC classification

Primary: 60G57: Random measures
Secondary: 62E15: Exact distribution theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 4 , December 2002 , pp. 764 - 774
Copyright
Copyright © Applied Probability Trust 2002 

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References

[1]. Carlton, M. (1999). Applications of the two-parameter Poisson–Dirichlet distribution. Doctoral Thesis, University of California, Los Angeles.Google Scholar
[2]. Ewens, W. J. (1972). The sampling theory of selectively neutral alleles. Theory Pop. Biol. 3, 87–112.Google Scholar
[3]. Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1, 209–230.Google Scholar
[4]. Hansen, B., and Pitman, J. (2000). Prediction rules for exchangeable sequences related to species sampling. Tech. Rep. 520, Department of Statistics, University of California, Berkeley. Statist. Prob. Lett. 46, 251–256.CrossRefGoogle Scholar
[5]. McCloskey, J. W. (1965). A model for the distribution of individuals by species in an environment. Doctoral Thesis, Michigan State University.Google Scholar
[6]. Perman, M. (1990). Random discrete distributions derived from subordinators. Doctoral Thesis, University of California, Berkeley.Google Scholar
[7]. Perman, M., Pitman, J., and Yor, M. (1992). Size-biased sampling of Poisson point processes and excursions. Prob. Theory Relat. Fields 92, 21–39.Google Scholar
[8]. Pitman, J. (1995). Exchangeable and partially exchangeable random partitions. Prob. Theory Relat. Fields 102, 145–158.Google Scholar
[9]. Pitman, J. (1996). Random discrete distributions invariant under size-biased permutation. Adv. Appl. Prob. 28, 525–539.CrossRefGoogle Scholar
[10]. Pitman, J. (1996). Some developments of the Blackwell–MacQueen urn scheme. In Statistics, Probability, and Game Theory (IMS Lecture Notes Monogr. 30), Institute of Mathematical Statistics, Hayward, CA, pp. 245–267.Google Scholar
[11]. Pitman, J. (1999). Coalescents with multiple collisions. Tech. Rep. 495, Department of Statistics, University of California, Berkeley. Ann. Prob. 27, 1870–1902.Google Scholar
[12]. Pitman, J., and Yor, M. (1997). The two-parameter Poisson–Dirichlet distribution derived from a stable subordinator. Ann. Prob. 25, 855–900.CrossRefGoogle Scholar
[13]. Sethuraman, J. (1994). A constructive definition of Dirichlet priors. Statist. Sinica 4, 639–650.Google Scholar
[14]. Sethuraman, J., and Tiwari, R. C. (1982). Convergence of Dirichlet measures and the interpretation of their parameter. In Statistical Decision Theory and Related Topics, III, Vol. 2, eds Gupta, S. S. and Berger, J. O., Academic Press, London, pp. 305–315.Google Scholar
[15]. Zwillinger, D. (ed.) (1996). Standard Mathematical Tables and Formulae, 30th edn. CRC Press, Boca Raton, FL.Google Scholar