A new method to assess Monte Carlo convergence
The central limit theorem can be applied to a Monte Carlo solution if the following two requirements are satisfied: (1) the random variable has a finite mean and a finite variance; and (2) the number N of independent observations grows large. When these are satisfied, a confidence interval based on the normal distribution with a specified coverage probability can be formed. The first requirement is generally satisfied by the knowledge of the type of Monte Carlo tally being used. The Monte Carlo practitioner has only a limited number of marginally quantifiable methods that use sampled values to assess the fulfillment of the second requirement; e.g., statistical error reduction proportional to 1[radical]N with error magnitude guidelines. No consideration is given to what has not yet been sampled. A new method is presented here to assess the convergence of Monte Carlo solutions by analyzing the shape of the empirical probability density function (PDF) of history scores, f(x), where the random variable x is the score from one particle history and [integral][sub [minus][infinity]][sup [infinity]] f(x) dx = 1. Since f(x) is seldom known explicitly, Monte Carlo particle random walks sample f(x) implicitly. Unless there is a largest possible history score, the empirical f(x) must eventually decrease more steeply than l/x[sup 3] for the second moment ([integral][sub [minus][infinity]][sup [infinity]] x[sup 2]f(x) dx) to exist.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE; USDOE, Washington, DC (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 6522167
- Report Number(s):
- LA-UR-93-1446; CONF-9304131-3; ON: DE93012667
- Resource Relation:
- Conference: Advanced Monte Carlo computer programs for radiation transport, Saclay (France), 27-29 Apr 1993
- Country of Publication:
- United States
- Language:
- English
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