SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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New adaptive method for variance reduction using approximating martingales

T. Badowski

Abstract
Approximating martingales method [1] is a variant of control variates method which can be used to reduce the variance of estimators of certain quantities defined for Markov chains, including their expected hitting times of sets. We introduce a new method for choosing adaptively the function $u$ [2] needed to construct the approximating martingale, to reduce the variance. As opposed to the well-known sample variance minimization method [2], the new method can be applied even when the number of performed simulations is lower than the number of basis functions used in the linear parametrization of $u$. In our numerical experiments we demonstrate that the new method can achieve on average high variance reductions and that it can significantly outperform the sample variance minimization method.

Bibliography
[1] S. G. Henderson and P. W. Glynn Approximating martingales for variance reduction in Markov process simulation, Math. Oper. Res., 27 (2002), pp. 253-271.
[2] S. Kim and S. G. Henderson, Adaptive control variates, Proceedings of the 2004 Winter Simulation Conference, 2004, pp. 621-629.

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