On the Poisson Equation For Metropolis-Hastings chains

Aleksandar Mijatovic; Jure Vogrinc

On the Poisson Equation For Metropolis-Hastings chains

Aleksandar Mijatovic, Jure Vogrinc

Mathematics

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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)Pki=1 F(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.

Original language	English
Pages (from-to)	2401-2428
Journal	BERNOULLI
Volume	24
Issue number	3
Early online date	19 Apr 2017
Publication status	E-pub ahead of print - 19 Apr 2017

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On the Poisson Equation_MIJATOVIC_Accepted 2017_GREEN AAM
Published in Bernoulli Journal, http://www.bernoulli-society.org/index.php/publications/bernoulli-journal, © International Statistical Institute/Bernoulli Society for Mathematical Statistics and Probability
Accepted author manuscript, 520 KBLicence: Other

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title = "On the Poisson Equation For Metropolis-Hastings chains",

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)Pki=1 F(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.",

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AU - Vogrinc, Jure

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N2 - 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)Pki=1 F(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.

AB - 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)Pki=1 F(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.

M3 - Article

SN - 1350-7265

VL - 24

SP - 2401

EP - 2428

JO - BERNOULLI

JF - BERNOULLI

IS - 3

ER -

On the Poisson Equation For Metropolis-Hastings chains

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