sampling In order to identify successful importance sampling techniques, it is useful to be able to quantify the run-time savings due to the use of the importance sampling approach. The performance measure commonly used is , and this can be interpreted as the speed-up factor by which the importance sampling estimator achieves the same precision as the MC estimator. This has to be computed empirically since the estimator variances are not likely to be analytically possible when their mean is intractable. Other useful concepts in quantifying an importance sampling estimator are the variance bounds and the notion of asymptotic efficiency. One related measure is the so-called Effective Sample Size (ESS). Variance cost function Variance is not the only possible cost function for a simulation, and other cost functions, such as the mean absolute deviation, are used in various statistical applications. Nevertheless, the variance is the primary cost function addressed in the literature, probably due to the use of variances in confidence intervals and in the performance measure . An associated issue is the fact that the ratio overestimates the run-time savings due to importance sampling since it does not include the extra computing time required to compute the weight function. Hence, some people evaluate the net run-time improvement by various means. Perhaps a more serious overhead to importance sampling is the time taken to devise and program the technique and analytically derive the desired weight function. Multiple and adaptive importance sampling When different proposal distributions, , are jointly used for drawing the samples different proper weighting functions can be employed (e.g., see ). In an adaptive setting, the proposal distributions, , and are updated each iteration of the adaptive importance sampling algorithm. Hence, since a population of proposal densities is used, several suitable combinations of sampling and weighting schemes can be employed. See also Monte Carlo method Variance reduction Stratified sampling Recursive stratified sampling VEGAS algorithm Particle filter — a sequential Monte Carlo method, which uses importance sampling Auxiliary field Monte Carlo Rejection sampling Variable bitrate — a common audio application of importance sampling Notes References External links Sequential Monte Carlo Methods (Particle Filtering) homepage on University of Cambridge Introduction to importance sampling in rare-event simulations European journal of Physics. PDF document. Adaptive monte carlo methods for rare event simulation: adaptive monte carlo methods for rare event simulations Winter Simulation Conference Monte Carlo methods Variance reduction Stochastic simulation