Fair-Coverage Monte Carlo Generation of Monotonic Functions within Envelopes


T. K. Satish Kumar

Knowledge Systems Laboratory Stanford University tksk@ksl.stanford.edu


Abstract: The Monte Carlo technique is an alternative to semi-quantitative simulation of incompletely known differential equations. Here, a large number of ODEs matching the given QDE are randomly generated making use of the available semi-quantitative information. Each ODE is then numerically integrated and conclusions are drawn from the family of results produced. Maintaining fair-coverage (or true randomness) is important for producing unbiased conclusions when we randomly generate monotonic functions matching the original incomplete specifications in the numerical integration phase of these techniques. Earlier attempts did not ensure fair-coverage in a theoretical sense. We provide a hierarchy of algorithms (exponential in number) to do this when envelopes for the monotonic functions are specified. These algorithms can be ranked according to increasing degrees of nearness to fair-coverage and decreasing computational tractability. The appropriate algorithm can then be selected from this hierarchy to suit the requirements of the problem.


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