A Universal Prior Distribution for Bayesian Consistency of Non parametric Procedures
(2015) In Communications in Statistics: Theory and Methods 44(5). p.972982 Abstract
 The introduction of the Hausdorff alphaentropy in Xing (2008a), Xing (2008b), Xing (2010), Xing (2011), and Xing and Ranneby (2009) has lead a series of improvements of wellknown results on posterior consistency. In this paper we discuss an application of the Hausdorff aentropy. 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 alphaentropy in Xing (2008a), Xing (2008b), Xing (2010), Xing (2011), and Xing and Ranneby (2009) has lead a series of improvements of wellknown results on posterior consistency. In this paper we discuss an application of the Hausdorff aentropy. 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:
http://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, Infinitedimensional 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
 03610926
 DOI
 10.1080/03610926.2012.750361
 language
 English
 LU publication?
 yes
 id
 bce2bfa2ae0740e28a84220d3092fa6e (old id 5293877)
 date added to LUP
 20150424 15:48:16
 date last changed
 20170101 03:33:01
@article{bce2bfa2ae0740e28a84220d3092fa6e, abstract = {The introduction of the Hausdorff alphaentropy in Xing (2008a), Xing (2008b), Xing (2010), Xing (2011), and Xing and Ranneby (2009) has lead a series of improvements of wellknown results on posterior consistency. In this paper we discuss an application of the Hausdorff aentropy. 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 = {03610926}, keyword = {Density function,Hausdorff entropy,Infinitedimensional model,Posterior consistency}, language = {eng}, number = {5}, pages = {972982}, 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}, }