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Sufficient conditions for Bayesian consistency

Xing, Yang LU and Ranneby, Bo (2009) In Journal of Statistical Planning and Inference 139(7). p.2479-2489
Abstract
We introduce the Hausdorff α-entropy to study the strong Hellinger consistency of posterior distributions. We obtain general Bayesian consistency theorems which extend the well-known results of Barron et al. [1999. The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27, 536–561] and Ghosal et al. [1999. Posterior consistency of Dirichlet mixtures in density estimation. Ann. Statist. 27, 143–158] and Walker [2004. New approaches to Bayesian consistency. Ann. Statist. 32, 2028–2043]. As an application we strengthen previous results on Bayesian consistency of the (normal) mixture models.
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author
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publishing date
type
Contribution to journal
publication status
published
subject
keywords
Infinite-dimensional model, Sieve, Posterior distribution, Hellinger consistency
in
Journal of Statistical Planning and Inference
volume
139
issue
7
pages
2479 - 2489
publisher
North-Holland
external identifiers
  • scopus:62049084447
ISSN
1873-1171
DOI
10.1016/j.jspi.2008.11.008
language
English
LU publication?
no
id
9f3000f6-98b6-4328-bdc7-969e147bb0b2 (old id 1465066)
alternative location
http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6V0M-4V1TXRG-2-1&_cdi=5650&_user=745831&_orig=search&_coverDate=07%2F01%2F2009&_sk=998609992&view=c&wchp=dGLzVtz-zSkWA&_valck=1&md5=26ae78f4b2906952bdac231182963eba&ie=/sdarticle.pdf
date added to LUP
2016-04-01 12:26:29
date last changed
2025-04-04 14:49:17
@article{9f3000f6-98b6-4328-bdc7-969e147bb0b2,
  abstract     = {{We introduce the Hausdorff α-entropy to study the strong Hellinger consistency of posterior distributions. We obtain general Bayesian consistency theorems which extend the well-known results of Barron et al. [1999. The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27, 536–561] and Ghosal et al. [1999. Posterior consistency of Dirichlet mixtures in density estimation. Ann. Statist. 27, 143–158] and Walker [2004. New approaches to Bayesian consistency. Ann. Statist. 32, 2028–2043]. As an application we strengthen previous results on Bayesian consistency of the (normal) mixture models.}},
  author       = {{Xing, Yang and Ranneby, Bo}},
  issn         = {{1873-1171}},
  keywords     = {{Infinite-dimensional model; Sieve; Posterior distribution; Hellinger consistency}},
  language     = {{eng}},
  number       = {{7}},
  pages        = {{2479--2489}},
  publisher    = {{North-Holland}},
  series       = {{Journal of Statistical Planning and Inference}},
  title        = {{Sufficient conditions for Bayesian consistency}},
  url          = {{http://dx.doi.org/10.1016/j.jspi.2008.11.008}},
  doi          = {{10.1016/j.jspi.2008.11.008}},
  volume       = {{139}},
  year         = {{2009}},
}