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Review theoretical methods for constructing prior distributions over spaces of probability measures for use in Bayesian nonparametric inference.

July 1, 1974The Annals of StatisticsOpen Access

Prior Distributions on Spaces of Probability Measures

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Authors

TFThomas S. FergusonUniversity of Massachusetts Boston

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Implication

Methodological review reveals construction methods for priors on probability spaces, highlighting Dirichlet, tailfree, and neutral-to-the-right processes in Bayesian nonparametrics.

Key Points

Review theoretical methods for constructing prior distributions over spaces of probability measures for use in Bayesian nonparametric inference.
Examined mathematical foundations for defining random probability measures on general spaces.
Focused analysis on Dirichlet processes, tailfree processes, and processes neutral to the right.
Surveyed practical and statistical applications of these prior distributions in inference tasks.
Characterized Dirichlet processes as tractable and analytically convenient baseline priors for infinite-dimensional inference.
Demonstrated that tailfree and neutral-to-the-right processes provide generalized alternatives that support diverse dependence structures.
Outlined specific implementation strategies for applying these random measures to nonparametric estimation and survival modeling.

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Thomas S. Ferguson (1974) studied this question.

synapsesocial.com/papers/6a11ddec4a30fb84f7a568e4 https://doi.org/10.1214/aos/1176342752

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Implication

Methodological review reveals construction methods for priors on probability spaces, highlighting Dirichlet, tailfree, and neutral-to-the-right processes in Bayesian nonparametrics.

Prior Distributions on Spaces of Probability Measures

Discussion

Member takes

Implication

Key Points

Cite This Study

Prior Distributions on Spaces of Probability Measures

Discussion

Member takes

Implication

Key Points

Cite This Study

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