Integrated Variance Reduction Strategies for Simulation

Abstract

We develop strategies for integrated use of certain well-known variance reduction techniques to estimate a mean response in a finite-horizon simulation experiment. The building blocks for these integrated variance reduction strategies are the techniques of conditional expectation, correlation induction (including antithetic variates and Latin hypercube sampling), and control variates; and all pairings of these techniques are examined. For each integrated strategy, we establish sufficient conditions under which that strategy will yield a smaller response variance than its constituent variance reduction techniques will yield individually. We also provide asymptotic variance comparisons between many of the methods discussed, with emphasis on integrated strategies that incorporate Latin hypercube sampling. An experimental performance evaluation reveals that in the simulation of stochastic activity networks, substantial variance reductions can be achieved with these integrated strategies. Both the theoretical and experimental results indicate that superior performance is obtained via joint application of the techniques of conditional expectation and Latin hypercube sampling.

Chapter 10 A Hilbert Space Approach to Variance Reduction

“…In this section we address the method of conditional Monte Carlo, paying special attention to its connection with control variates; we follow Avramidis and Wilson (1996), and Loh (1995).…”

“…Avramidis and Wilson (1996), and Loh (1995), generalize this approach: Let Z be a zero-mean random variable in L 2 (Ω, F, P), and X a random variable in L 2 (Ω, F, P) for which both E(Y |X) and E(Z|X) can be determined. Then sampling from…”

“…In particular, Loh (1995) considers the case of Z = X almost surely in (35), and Avramidis and Wilson (1996) fix λ 1 = 1 and λ 3 = 0 in (35). From the norm perspective,…”

“…We rely on Mathé (2000), which gives a good account of LHS from a Hilbert space point of view. Avramidis and Wilson (1996) is also a valuable reference for the issues we consider.…”

Accounting for input-model and input-parameter uncertainties in simulation

“…2. Correlated sampling schemes for improving the efficiency of the BMA-based simulation replication algorithm require further exploration; see, for example, Avramidis and Wilson (1996). 3.…”