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On nonparametric Bayesian inference for the distribution of a random sample
Author(s) -
Gelfand Alan E.,
Mukhopadhyay Saurabh
Publication year - 1995
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315384
Subject(s) - nonparametric statistics , inference , sample (material) , bayesian inference , bayesian probability , statistics , mathematics , computer science , sampling distribution , artificial intelligence , econometrics , chemistry , chromatography
The nonparametric Bayesian approach for inference regarding the unknown distribution of a random sample customarily assumes that this distribution is random and arises through Dirichlet‐process mixing. Previous work within this setting has focused on the mean of the posterior distribution of this random distribution, which is the predictive distribution of a future observation given the sample. Our interest here is in learning about other features of this posterior distribution as well as about posteriors associated with functionals of the distribution of the data. We indicate how to do this in the case of linear functionals. An illustration, with a sample from a Gamma distribution, utilizes Dirichlet‐process mixtures of normals to recover this distribution and its features.