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Polya Trees and Random Distributions
Open accessAbstract
Trees of Polya urns are used to generate sequences of exchangeable random variables. By a theorem of de Finetti each such sequence is a mixture of independent, identically distributed variables and the mixing measure can be viewed as a prior on distribution functions. The collection of these Polya tree priors forms a convenient conjugate family which was mentioned by Ferguson and includes the Dirichlet processes of Ferguson. Unlike Dirichlet processes, Polya tree priors can assign probability 1 to the class of continuous distributions. This property and a few others are investigated.
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Cited by
Combinatorial Stochastic Processes
(2006) · Lecture Notes in Mathematics · doi:10.1007/b11601500 · Cited by 935
A Survey on Explainable Anomaly Detection
Li, Z., Zhu, Y., & Van Leeuwen, M. (2024) · ACM Transactions on Knowledge Discovery from Data · doi:10.1145/3609333 · Cited by 139
“Specifically, the Mondrian Process [177] is a family of hierarchical binary partitions of data and the Pólya Tree [136] is a non-parametric approach that can estimate the density function of binary partitions.”
Method
Metadata
- Authors
- Mauldin, R. D., Sudderth, W. D., & Williams, S. C.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1992-09-01
- Volume
- 20
- Issue
- 3
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2074178102
- Cited by
- 216
- References
- 0
- FWCI
- 1.34
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Mauldin, R. D., Sudderth, W. D., & Williams, S. C. (1992). Polya Trees and Random Distributions. The Annals of Statistics. https://doi.org/10.1214/aos/1176348766
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
