The Economics of Variance Reduction in Sequential Manufacturing

The purpose of the present work is to quantify parametric uncertainty in the Rothermel wildland fire spread model (implemented in software such as BehavePlus3 and FARSITE), which is undoubtedly among the most widely used fire spread models in the United States. This model consists of a non-linear system of equations that relates environmental variables (input parameter groups) such as fuel type, fuel moisture, terrain, and wind to describe the fire environment. This model predicts important fire quantities (output parameters) such as the head rate of spread, spread direction, effective wind speed, and fireline intensity. The proposed method, which we call sensitivity derivative enhanced sampling, exploits sensitivity derivative information to accelerate the convergence of the classical Monte Carlo method. Coupled with traditional variance reduction procedures, it offers up to two orders of magnitude acceleration in convergence, which implies that two orders of magnitude fewer samples are required for a given level of accuracy. Thus, it provides an efficient method to quantify the impact of input uncertainties on the output parameters.

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Variance reduction for sequential sampling in stochastic programming

Annals of Operations Research ◽

10.1007/s10479-020-03908-x ◽

2021 ◽

Author(s):

Jangho Park ◽

Rebecca Stockbridge ◽

Güzin Bayraksan

Keyword(s):

Stochastic Programming ◽

Variance Reduction ◽

Sequential Sampling

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Variance reduction in Ueno's method and cylinder sampling for forest volume estimation

Canadian Journal of Forest Research ◽

10.1139/x95-193 ◽

1995 ◽

Vol 25 (11) ◽

pp. 1783-1794 ◽

Cited By ~ 3

Author(s):

Thomas B. Lynch

Keyword(s):

Computer Simulation ◽

Variance Reduction ◽

Volume Estimation ◽

Critical Height ◽

Volume Estimate ◽

Individual Tree ◽

Stand Volume ◽

Reduction Techniques ◽

Antithetic Variates ◽

Volume Equation

Three basic techniques are proposed for reducing the variance of the stand volume estimate provided by cylinder sampling and Ueno's method. Ueno's method is based on critical height sampling but does not require measurement of critical heights. Instead, a count of trees whose critical heights are less than randomly generated heights is used to estimate stand volume. Cylinder sampling selects sample trees for which randomly generated heights fall within cylinders formed by tree heights and point sampling plot sizes. The methods proposed here for variance reduction in cylinder sampling and Ueno's method are antithetic variates, importance sampling, and control variates. Cylinder sampling without variance reduction was the most efficient of 12 methods compared in computer simulation that used estimated measurement times. However, cylinder sampling requires knowledge of a combined variable individual tree volume equation. Of the three variance reduction techniques applied to Ueno's method, antithetic variates performed best in computer simulation.

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