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Density estimation for the Metropolis-Hastings algorithm

Sköld, Martin LU and Roberts, G O (2003) In Scandinavian Journal of Statistics 30(4). p.699-718
Abstract
Kernel density estimation is an important tool in visualizing posterior densities from Markov chain Monte Carlo output. It is well known that when smooth transition densities exist, the asymptotic properties of the estimator agree with those for independent data. In this paper, we show that because of the rejection step of the Metropolis-Hastings algorithm, this is no longer true and the asymptotic variance will depend on the probability of accepting a proposed move. We find an expression for this variance and apply the result to algorithms for automatic bandwidth selection.
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 estimation, Metropolis-Hastings algorithm
in
Scandinavian Journal of Statistics
volume
30
issue
4
pages
699 - 718
publisher
Wiley-Blackwell
external identifiers
  • wos:000186460900004
  • scopus:0242458502
ISSN
1467-9469
DOI
10.1111/1467-9469.00359
language
English
LU publication?
yes
id
1ad41b2a-9310-4a50-a994-e80a0157f1fe (old id 295845)
date added to LUP
2007-09-21 16:40:39
date last changed
2018-05-29 10:50:16
@article{1ad41b2a-9310-4a50-a994-e80a0157f1fe,
  abstract     = {Kernel density estimation is an important tool in visualizing posterior densities from Markov chain Monte Carlo output. It is well known that when smooth transition densities exist, the asymptotic properties of the estimator agree with those for independent data. In this paper, we show that because of the rejection step of the Metropolis-Hastings algorithm, this is no longer true and the asymptotic variance will depend on the probability of accepting a proposed move. We find an expression for this variance and apply the result to algorithms for automatic bandwidth selection.},
  author       = {Sköld, Martin and Roberts, G O},
  issn         = {1467-9469},
  keyword      = {density estimation,Metropolis-Hastings algorithm},
  language     = {eng},
  number       = {4},
  pages        = {699--718},
  publisher    = {Wiley-Blackwell},
  series       = {Scandinavian Journal of Statistics},
  title        = {Density estimation for the Metropolis-Hastings algorithm},
  url          = {http://dx.doi.org/10.1111/1467-9469.00359},
  volume       = {30},
  year         = {2003},
}