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Methods of reducing sample size in Monte Carlo computations. (English) Zbl 1414.90373

Summary: This paper deals with the problem of increasing the efficiency of Monte Carlo calculations. The methods of doing so permit one to reduce the sample size required to produce estimates of a fixed level of accuracy or, alternatively, to increase the accuracy of the estimates for a fixed cost of computation. Few theorems are known with regard to optimal sampling schemes, but several helpful ideas of very general applicability are available for use in designing Monte Carlo sampling schemes. Three of these ideas are discussed and illustrated in simple cases. These ideas are (1) correlation of samples, (2) importance sampling, and (3) statistical estimation.

MSC:

90C90 Applications of mathematical programming
65K05 Numerical mathematical programming methods
65C05 Monte Carlo methods
62D05 Sampling theory, sample surveys
62P20 Applications of statistics to economics
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