Latin Hypercube and Monte Carlo Sampling: When is the distinction important?

Latin Hypercube analysisWhen using @RISK (Monte Carlo software for risk analysis and risk assessment), a user may choose between the Monte Carlo (MC) and Latin Hypercube (LH) sampling types.  LH sampling involves a stratification of the input distribution i.e. the cumulative curve is divided into equal intervals on the cumulative probability scale (0 to 1.0).  In theory, LH sampling would create a more representative sampling of the distribution.  It would avoid potential non-representative clustering of sampled values (particularly when small sample sizes are drawn i.e. a small number of iterations is used), and would also ensure that tail samples of the input distributions are drawn (e.g. for 1000 iterations, exactly one value above the P99.9 would be drawn, whereas for MC sampling either none, one or several samples may be drawn).  In general, LH sampling would be favourable when testing and developing a model (running only a small number of iterations), or when running a model that is so large that only a small number of iterations can be conducted.  It can also be used to force the sampling of tails of distributions, although it should be remembered that LH stratification applies to each individual input variable, and it would not force the simultaneous sampling of tail values for more than one input.

Dr. Michael Rees
Director of Training and Consulting

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