Show full list of Contributed Talks Show talk context (CS07)

__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.