Descriptive Sampling: A Better Approach to Monte Carlo Simulation

Abstract

Although simple random sampling is the standard sampling procedure in Monte Carlo simulation, such practice is questioned in this paper. In any Monte Carlo application, sampled distributions are assumed to be known. Using simple random sampling, sample histograms or, equivalently, sample moments will vary at random, thus producing an imprecise description of the known input distribution, and consequently increasing the variance of simulation estimates. This problem can be avoided with descriptive sampling, here proposed as a more appropriate approach in Monte Carlo simulation than simple random sampling. Descriptive sampling is based on a deterministic and purposive selection of the sample values—in order to conform as closely as possible to the sampled distribution—and the random permutation of these values. As such, it represents a fundamental conceptual change in Monte Carlo sampling, departing from the ‘principle’ that sample values must be randomly generated in order to describe random behaviour. The basis of this new idea, examples of its use and empirical results are presented.