
In this very interesting paper an extension of the alias sampling technique for distribution functions depending on a number of parameters is developed. It takes advantage of modern computer architectures with large amount of cheap memory, by using discrete representations of probability distribution functions. The sampling is done by fast interpolation techniques involving only elementary logical and arithmetical operations, allowing thus one to keep a higher degree of accuracy as the grid spacing is controlled by the user. By this method it is possible to obtyain the values of interest by direct interpolation between the sampled values with the same set of random numbers for the grid values of the parameters adjacent to the values of interest. Sampling tests carried for the case of Molière electron multi-scatter angle distribution show that this method can be successfully used in Monte Carlo codes for sampling complex probability distributions. This method can be successfully used as an alternative to the sampling arrangements commonly used in Monte Carlo codes where, for complex probability distributions, from case to case, after a careful study of function properties, combinations of sampling techniques (e.g. superposition, rejection and inverse function methods) are used. The method proposed here allows one to develop flexible Monte Carlo simulation codes, while the application of specific sampling techniques like those mentioned above makes the resultant code strongly dependent on the theories used.
Monte Carlo method, probability distribution functions, \(n\)-body potential quantum scattering theory, random variable, alias sampling technique, Sampling theory, sample surveys, Monte Carlo methods, fast interpolation techniques, Applications of statistics to physics, Molière multi-scatter angle distribution
Monte Carlo method, probability distribution functions, \(n\)-body potential quantum scattering theory, random variable, alias sampling technique, Sampling theory, sample surveys, Monte Carlo methods, fast interpolation techniques, Applications of statistics to physics, Molière multi-scatter angle distribution
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