Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-25T14:07:19.069Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  14 July 2016

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: [email protected]

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2002 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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, 87112.Google Scholar
[3]. Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1, 209230.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, 251256.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, 2139.Google Scholar
[8]. Pitman, J. (1995). Exchangeable and partially exchangeable random partitions. Prob. Theory Relat. Fields 102, 145158.Google Scholar
[9]. Pitman, J. (1996). Random discrete distributions invariant under size-biased permutation. Adv. Appl. Prob. 28, 525539.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. 245267.Google Scholar
[11]. Pitman, J. (1999). Coalescents with multiple collisions. Tech. Rep. 495, Department of Statistics, University of California, Berkeley. Ann. Prob. 27, 18701902.Google Scholar
[12]. Pitman, J., and Yor, M. (1997). The two-parameter Poisson–Dirichlet distribution derived from a stable subordinator. Ann. Prob. 25, 855900.CrossRefGoogle Scholar
[13]. Sethuraman, J. (1994). A constructive definition of Dirichlet priors. Statist. Sinica 4, 639650.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. 305315.Google Scholar
[15]. Zwillinger, D. (ed.) (1996). Standard Mathematical Tables and Formulae, 30th edn. CRC Press, Boca Raton, FL.Google Scholar