On the Poisson equation for Metropolis Hastings chains
File(s)
Accepted version
Author(s)
Vogrinc, J
Mijatovic, A
Type
Journal Article
Abstract
Abstract.
This paper defines an approximation scheme for a solution of t
he Poisson equation of
a geometrically ergodic Metropolis-Hastings chain Φ. The s
cheme is based on the idea of weak
approximation and gives rise to a natural sequence of contro
l variates for the ergodic average
S
k
(
F
) = (1
/k
)
∑
k
i
=1
F
(Φ
i
), 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 converg
ence. Numerical examples in the case
of a double-well potential are discussed.
This paper defines an approximation scheme for a solution of t
he Poisson equation of
a geometrically ergodic Metropolis-Hastings chain Φ. The s
cheme is based on the idea of weak
approximation and gives rise to a natural sequence of contro
l variates for the ergodic average
S
k
(
F
) = (1
/k
)
∑
k
i
=1
F
(Φ
i
), 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 converg
ence. Numerical examples in the case
of a double-well potential are discussed.
Date Issued
2018-02-02
Date Acceptance
2017-04-21
Citation
Bernoulli, 2018, 24 (3), pp.2401-2428
ISSN
1350-7265
Publisher
Bernoulli Society for Mathematical Statistics and Probability
Start Page
2401
End Page
2428
Journal / Book Title
Bernoulli
Volume
24
Issue
3
Copyright Statement
© 2018 ISI/BS
Identifier
https://projecteuclid.org/euclid.bj/1517540478#abstract
Subjects
Statistics & Probability
0104 Statistics
1403 Econometrics
Publication Status
Published
Date Publish Online
2018-02-02