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arXiv · 1511.07464

On the Poisson equation for Metropolis-Hastings chains

Aleksandar Mijatovic·Jure Vogrinc
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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 $\Phi$. The approximations give rise to a natural sequence of control variates for the ergodic average $S_k(F)=(1/k)\sum_{i=1}^{k} F(\Phi_i)$, where $F$ is the force function in the Poisson equation. The main result of the paper shows that the sequence of the asymptotic variances (in the CLTs for the control-variate estimators) converges to zero and gives a rate of this convergence. Numerical examples in the case of a double-well potential are discussed.

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Aleksandar Mijatovic, Jure Vogrinc. 2015-11-23. On the Poisson equation for Metropolis-Hastings chains. https://arxiv.org/abs/1511.07464

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