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|In discussing this with Eric Wainwright,
Decisioneering's chief guru, in May 1999, I became more clear about how
the procedure should work. Here is a 2nd revised approach from what
was presented earlier on this page.
Crystal Ball® 2000 features Precision Control™, a stopping function that uses the "bootstrapping" method. They have applied for a patent on their algorithm, which I haven't seen. Precision Control can be used broadly in using other statistics in stopping rules.
Here is a stopping rule procedure to apply when Latin Hypercube Sampling (LHS) is used with Monte Carlo simulation.
If you need precision better than the SEM, run more trials in multiples of Sample Size. Recall that a 68% confidence interval for the Expected Value is the overall sample mean ± SEM.
This is the best stopping rule that I can offer at the present. Perhaps Eric's method in Crystal Ball is better. Note that it is not unusual that LHS require only 1/5 as many trials as traditional Monte Carlo sampling.
The Student-t distribution may provide an additional refinement in correcting the sample standard deviation for the small number of data values.
|Update: In searching palisade.com for a technique related to LHS, I came across a note in their knowledge base. "6.23 Confidence intervals in @RISK" http://kb.palisade.com/index.php?pg=kb.page&id=124 This describes a similar process and a published paper: Michael Stein, "Large Sample Properties of Simulations Using Latin Hypercube Sampling", Technometrics 29:2 [May 1987], pages 143-151, pay site still working 19-apr-16, from http://www.jstor.org/stable/1269769.)|
John Schuyler, January 1998. Revised 15-Sep-99, 26-Apr-00, and 19-Apr-16
Copyright © 1998-2016 by John R. Schuyler. All rights reserved. Permission to copy with reproduction of this notice.