We study control variate estimation where the control mean itself is estimated. Control variate estimation in simulation experiments can significantly increase sampling efficiency, and has traditionally been restricted to cases where the control has a known mean. In a previous paper (Schmeiser, Taaffe, and Wang 2000), we generalized the idea of control variate estimation to the case where the c...

\Knowledge of either analytical or numerical approximations should enable more eecient simulation estima-tors to be constructed." This principle seems intuitively plausible and certainly attractive, yet no completely satisfactory general methodology has been developed to exploit it. We present a new approach for Markov processes that relies on the construction of a martingale that is strongly c...

We present two improvements on the technique of importance sampling. First we show that importance sampling from a mixture of densities, using those densities as control variates, results in a useful upper bound on the asymptotic variance. That bound is a small multiple of the asymptotic variance of importance sampling from the best single component density. This allows one to beneet from the g...

This article details several procedures for using path control variates to improve the accuracy of simulation-based point and confidence-interval estimators of the mean completion time of a stochastic activity network (SAN). Because each path control variate is the duration of the corresponding directed path in the network from the source to the sink, the vector of selected path controls has bo...

We will demonstrate the utility of Monte Carlo integration by using this algorithm to calculate an estimate for . In order to improve this estimate, we will also demonstrate how a family of covariate functions can be used to reduce the variance. Finally, the optimal covariate function within this family is found numerically. 1. An Introduction to Monte Carlo Integration 1.1. Monte Carlo Integra...

Abstract Simulations have become an indispensable tool for accurate modelling of observables measured in galaxy surveys, but can be expensive if very large dynamic range scale is required. We describe how to combine Lagrangian perturbation theory models with N-body simulations reduce the effects finite computational volume prediction ensemble average properties within context control variates. ...

In this chapter we explain variance reduction techniques from the Hilbert space standpoint, in the terminating simulation context. We use projection ideas to explain how variance is reduced, and to link different variance reduction techniques. Our focus is on the methods of control variates, conditional Monte Carlo, weighted Monte Carlo, stratification, and Latin hypercube sampling.

Consider three different but related problems with auxiliary information: infinite population sampling or Monte Carlo with control variates, missing response with explanatory variables, and Poisson and rejective sampling with auxiliary variables. We demonstrate unified regression and likelihood estimators and study their second-order properties. The likelihood estimators are second-order unbias...

Predictions of the mean and covariance matrix summary statistics are critical for confronting cosmological theories with observations, not least likelihood approximations parameter inference. The price to pay accurate estimates is extreme cost running $N$-body hydrodynamics simulations. Approximate solvers, or surrogates, greatly reduce computational but can introduce significant biases, exampl...

Covariate shift classification problems can in principle be tackled by importanceweighting training samples. However, the sampling variance of the risk estimator is often scaled up dramatically by the weights. This means that during cross-validation when the importance-weighted risk is repeatedly evaluated suboptimal hyperparameter estimates are produced. We study the sampling variances of the ...