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Asymptotic frequentist coverage properties of Bayesian credible sets for sieve priors

Abstract:

We investigate the frequentist coverage properties of (certain) Bayesian credible sets in a general, adaptive, nonparametric framework. It is well known that the construction of adaptive and honest confidence sets is not possible in general. To overcome this problem (in context of sieve type of priors), we introduce an extra assumption on the functional parameters, the so-called “general polished tail” condition. We then show that under standard assumptions, both the hierarchical and empirica...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1214/19-AOS1881

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Institution:
University of Oxford
Division:
MPLS
Department:
Statistics
Oxford college:
Jesus College
Role:
Author
ORCID:
0000-0002-0998-6174
Publisher:
Institute of Mathematical Statistics Publisher's website
Journal:
Annals of Statistics Journal website
Volume:
48
Issue:
4
Pages:
2155-2179
Publication date:
2020-08-14
Acceptance date:
2019-06-09
DOI:
ISSN:
0090-5364
Source identifiers:
1023033
Language:
English
Keywords:
Pubs id:
pubs:1023033
UUID:
uuid:555390ea-7ab4-4fa1-92e0-9baf3bd0fa8d
Local pid:
pubs:1023033
Deposit date:
2019-06-26

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