McXtrace - An X-ray ray-trace simulation package

4.5  Accuracy of Monte Carlo simulations

When running a Monte Carlo, the meaningful quantities are obtained by integrating random events into a single value (e.g. flux), or onto an histogram grid. The theory [Jam80] shows that the accuracy of these estimates is a function of the space dimension \(d\) and the number of events \(N\). For large numbers \(N\), the central limit theorem provides an estimate of the relative error as \(1/\sqrt {N}\). However, the exact expression depends on the random distributions.

McXtrace uses a space with \(d=12\) parameters to describe x-rays (position, wavevector, weight, polarisation, phase, time). We show in Table 4.1 a rough estimate of the accuracy on integrals as a function of the number of records reaching the integration point. This stands both for integrated flux, as well as for histogram bins - for which the number of events per bin should be used for \(N\).

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