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In order to obtain a large number of samples, one needs to perform the same number of inversions of the distribution.
One possible way to reduce the number of inversions while obtaining a large number of samples is the application of the so-called Stochastic Collocation Monte Carlo sampler (SCMC sampler) within a [[polynomial chaos]] expansion framework. This allows us to generate any number of Monte Carlo samples with only a few inversions of the original distribution with independent samples of a variable for which the inversions are analytically available, for example the standard normal variable.<ref>L.A. Grzelak, J.A.S. Witteveen, M. Suarez, and C.W. Oosterlee. The stochastic collocation Monte Carlo sampler: Highly efficient sampling from “expensive” distributions. https://ssrn.com/abstract=2529691</ref>
== Software implementations ==
There are software implementations available for applying the inverse sampling method by using numerical approximations of the inverse in the case that it is not available in closed form. For example, an approximation of the inverse can be computed if the user provides some information about the distributions such as the PDF <ref>
{{cite journal | last1 = Derflinger | first1 = Gerhard | last2 = Hörmann | first2 = Wolfgang | last3 = Leydold | first3 = Josef | title = Random variate generation by numerical inversion when only the density is known | journal = ACM Transactions on Modeling and Computer Simulation | date = 2010 | volume = 20 | issue = 4 | doi = 10.1145/945511.945517}}</ref> or the CDF.
* C library UNU.RAN <ref>https://statmath.wu.ac.at/unuran/index.html</ref>
* R library Runuran <ref>https://cran.r-project.org/package=Runuran</ref>
* Python subpackage sampling in scipy.stats <ref>https://docs.scipy.org/doc/scipy/reference/stats.sampling.html</ref><ref>
{{cite journal | last1 = Baumgarten | first1 = Christoph | last2 = Patel | first2 = Tirth | title = Automatic random variate generation in Python | journal = Proceedings of the 21st Python in Science Conference | date = 2022 | doi = 10.25080/majora-212e5952-007}}</ref>
== See also ==
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