A Universal Prior Distribution for Bayesian Consistency of Non parametric Procedures
(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:
https://lup.lub.lu.se/record/5293877
- author
- Xing, Yang LU
- organization
- publishing date
- 2015
- 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
- 2016-04-01 10:23:55
- date last changed
- 2022-04-27 21:40:45
@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}},
keywords = {{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}},
doi = {{10.1080/03610926.2012.750361}},
volume = {{44}},
year = {{2015}},
}