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On the Poisson equation for Metropolis–Hastings chains
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Mijatović, Aleksandar and Vogrinc, Jure (2018) On the Poisson equation for Metropolis–Hastings chains. Bernoulli, 24 (3). pp. 2401-2428. doi:10.3150/17-BEJ932 ISSN 1350-7265.
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Official URL: http://dx.doi.org/10.3150/17-BEJ932
Abstract
This paper defines an approximation scheme for a solution of the Poisson equation of a geometrically ergodic Metropolis–Hastings chain Φ. The scheme is based on the idea of weak approximation and gives rise to a natural sequence of control variates for the ergodic average Sk(F)=(1/k)∑ki=1F(Φi), where F is the force function in the Poisson equation. The main results show that the sequence of the asymptotic variances (in the CLTs for the control-variate estimators) converges to zero and give a rate of this convergence. Numerical examples in the case of a double-well potential are discussed.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Bernoulli | ||||
Publisher: | Int Statistical Institute | ||||
ISSN: | 1350-7265 | ||||
Official Date: | 2 February 2018 | ||||
Dates: |
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Volume: | 24 | ||||
Number: | 3 | ||||
Page Range: | pp. 2401-2428 | ||||
DOI: | 10.3150/17-BEJ932 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Open Access Version: |
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