On the Poisson Equation for Metropolis-hastings Chains
نویسنده
چکیده
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) ∑k i=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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