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A Universal Prior Distribution for Bayesian Consistency of Non parametric Procedures

Xing, Yang LU (2015) In Communications in Statistics: Theory and Methods 44(5). p.972-982
Abstract
The introduction of the Hausdorff alpha-entropy in Xing (2008a), Xing (2008b), Xing (2010), Xing (2011), and Xing and Ranneby (2009) has lead a series of improvements of well-known results on posterior consistency. In this paper we discuss an application of the Hausdorff a-entropy. We construct a universal prior distribution such that the corresponding posterior distribution is almost surely consistent. The approach of the construction of this type of prior distribution is natural, but it works very well for all separable models. We illustrate such prior distributions by examples. In particular, we obtain that if the true density function is known to be some normal probability density function with unknown mean and unknown variance then... (More)
The introduction of the Hausdorff alpha-entropy in Xing (2008a), Xing (2008b), Xing (2010), Xing (2011), and Xing and Ranneby (2009) has lead a series of improvements of well-known results on posterior consistency. In this paper we discuss an application of the Hausdorff a-entropy. We construct a universal prior distribution such that the corresponding posterior distribution is almost surely consistent. The approach of the construction of this type of prior distribution is natural, but it works very well for all separable models. We illustrate such prior distributions by examples. In particular, we obtain that if the true density function is known to be some normal probability density function with unknown mean and unknown variance then without any additional assumption one can construct a prior distribution which leads to posterior consistency. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Density function, Hausdorff entropy, Infinite-dimensional model, Posterior consistency
in
Communications in Statistics: Theory and Methods
volume
44
issue
5
pages
972 - 982
publisher
Marcel Dekker
external identifiers
  • wos:000351220400007
  • scopus:84924940529
ISSN
0361-0926
DOI
10.1080/03610926.2012.750361
language
English
LU publication?
yes
id
bce2bfa2-ae07-40e2-8a84-220d3092fa6e (old id 5293877)
date added to LUP
2015-04-24 15:48:16
date last changed
2017-01-01 03:33:01
@article{bce2bfa2-ae07-40e2-8a84-220d3092fa6e,
  abstract     = {The introduction of the Hausdorff alpha-entropy in Xing (2008a), Xing (2008b), Xing (2010), Xing (2011), and Xing and Ranneby (2009) has lead a series of improvements of well-known results on posterior consistency. In this paper we discuss an application of the Hausdorff a-entropy. We construct a universal prior distribution such that the corresponding posterior distribution is almost surely consistent. The approach of the construction of this type of prior distribution is natural, but it works very well for all separable models. We illustrate such prior distributions by examples. In particular, we obtain that if the true density function is known to be some normal probability density function with unknown mean and unknown variance then without any additional assumption one can construct a prior distribution which leads to posterior consistency.},
  author       = {Xing, Yang},
  issn         = {0361-0926},
  keyword      = {Density function,Hausdorff entropy,Infinite-dimensional model,Posterior consistency},
  language     = {eng},
  number       = {5},
  pages        = {972--982},
  publisher    = {Marcel Dekker},
  series       = {Communications in Statistics: Theory and Methods},
  title        = {A Universal Prior Distribution for Bayesian Consistency of Non parametric Procedures},
  url          = {http://dx.doi.org/10.1080/03610926.2012.750361},
  volume       = {44},
  year         = {2015},
}