Abstract
The Monte Carlo Method is a very useful and versatile numerical technique that allows to solve a large variety of problems difficult to tackle by other procedures. Even though the central idea is to simulate experiments on a computer and make inferences from the “observed” sample, it is applicable to problems that do not have an explicit random nature; it is enough if they have an adequate probabilistic approach. In fact, a frequent use of Monte Carlo techniques is the evaluation of definite integrals that at first sight have no statistical nature but can be interpreted as expected values under some distribution. In this lecture we shall present and justify essentially all the procedures that are commonly used in particle physics and statistics leaving aside subjects like Markov Chains that deserve a whole lecture by themselves and for which only the relevant properties will be stated without demonstration.
Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin
J. Von Neumann
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For the examples in this lecture I have used RANMAR [5] that can be found, for instance, at the CERN Computing Library.
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Remember that if \(\mathrm{supp}(X)=\Omega {\subseteq }\mathcal{R}\), it is assumed that the density is \(p(x){{\varvec{1}}_{\Omega }(x)}\).
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Maña, C. (2017). Monte Carlo Methods. In: Probability and Statistics for Particle Physics. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-55738-0_3
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DOI: https://doi.org/10.1007/978-3-319-55738-0_3
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