Variance reduction

Fitzgerald, M. Picard, R. R. Silver, R. N., Monte Carlo transition dynamics and variance reduction, J. Stat. Phys. 1999, 98, 321-345... 

Wilson JR. 1984. Variance reduction techniques for digital simulation. Am J Math Manage Sci 4 277-312. 

FIG. 21-56 Dampening of feed fluctuation in a continuous mixer— variance reduction ratio (VRR). The efficiency of continuous mixing processes is described by the variance reduction ratio. The variances in concentration of inlet and outlet are compared. Tracer-feed oscillating with different periods T, main component feed at constant rate (20 g/s), mean residence time in the continuous mixer % = 44 s. a) Variation in time of SiC concentration dotted line at the entrance of the continuous mixer, bold line at the outlet of the continuous mixer, (h) Power density spectrum of SiC concentration. High variance reduction ratios are achieved if the period of the tracer feed is small compared to the mean residence time in the mixer... 

Ridge regression estimators are biased. The trade-off for stabilization and variance reduction in regression coefficient estimators is the bias in the estimators and the increase in the squared error. 

When the fluid-velocity-fluctuation-dissipation model in Eq. (4.104) is included, an additional variance reduction mechanism will be present. 

A transformation of the data giving an improved fit may sometimes be obtained by trial and error, but one or both of the following approaches is recommended. One may make a theoretical choice of transformation and test if it gives improved results - a regression that is more significant in analysis of variance, reduction in the number of outliers, residuals normally distributed. Alternatively the Box-Cox transformation method may be used. 

The goal of variance reduction is to decrease the error of a point estimate, which should lead to a smaller estimated standard error or a narrower confidence interval (see Section 8 for a discussion of measures of error). This section describes the variance reduction technique known as common random numbers (CRN), which is useful for reducing the error in comparing the expected performance of two or more systems. The presentation is based on Nelson (1987). 

A well-developed statistical inference of the estimators and exists (Rubinstein and Shapiro 1993). That inference aids in the construction of stopping rules, validation analysis, and error bounds for obtained solutions and, furthermore, suggests variance reduction methods that may substantially enhance the rate of convergence of the numerical procedure. For a discussion of this topic and an application to two-stage stochastic programming with recourse, we refer to Shapiro and Homem-de-Mello (1998). 

Simulation(s) (Continued) steady-state, 2471-2472 for teamwork training, 934 terminating, 2471 as training technology, 929 and transformability, 320 variance reduction in, 2492-2493 Simulation Dynamics, 2460 Simulation methods, 128 Simulation models, 1630 for client/server (C/S) system evaluation, 728-719... 

This simplified description has assumed that the exact physical probabilities are utilized to determine the outcome of every decision when this is done, the resulting simulation is termed an analog simulation. More sophisticated statistical treatments are included in modern computer codes that utilize nonphysical distributions with corrections (in a defined parficle weight) to keep the results of the simulation unbiased these can be shown to improve the efficiency of the simulation. These methods are called "variance reduction" methods, although this is somewhat of a misnomer because many of these methods increase efficiency by saving computer time, not by reducing variance. The exact theory and technique for doing this is beyond the scope of this handbook but is well described in Monte Carlo descriptions such as in Lewis and Miller (1993). 

Variance Reduction Techniques Importance Sampling (IS), Line Sampling (LS), etc. 

In spite of the arguments discussed above, the concept of design point in reUabil-ity analysis should not be discarded. Recent advances in the development of variance reduction techniques (Au 2008) have shown that the design point (associated with uncertainty in excitation) can be rather useful when interpreted as the excitation with minimum energy capable of driving the structural reponse towards a prescribed threshold level. But how to estimate the design point efficiently still remains an open issue, except for a small class of reliability problems, where exact or approximate solutions have been proposed. 

Among different monitoring techniques like Kalman filters and various Data Reconciliation schemes, Kalman filter presents good variance reduction, estimation of process variables and better tracking in dynamic changes of the process (Benqliiou et al 2002). This performance, however, varies with the position and quality (variance) of the sensors. This paper focuses on the determination of the optimal sensor placement for the use of Kalman filtering. 

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