Abstract
In this chapter we look into a collection of direct methods for random sampling. The term direct is used here to indicate that i.i.d. random draws with exactly the desired probability distribution are produced by applying a transformation that maps one (or many) realizations from the available random source into a realization from the target random variable. Most often, this transformation can be described as a deterministic map. However, we also include here techniques that rely on either discrete or continuous mixtures of densities and which can be interpreted as (pseudo)stochastic transformations of the random source.
Furthermore, many of the techniques proposed in the literature are found to be closely related when studied in sufficient detail. We pay here specific attention to some of these links, as they can be later exploited for the design of more efficient samplers, or simply to attain a better understanding of the field.
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- 1.
Note that \(\frac {\pi ^{m/2}}{\frac {m}{2}\Gamma \left (\frac {m}{2}\right )}\) is the volume of the unit sphere.
- 2.
Note that g(y) is always a proper normalized pdf. This can be easily proved integrating by parts twice.
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Martino, L., Luengo, D., Míguez, J. (2018). Direct Methods. In: Independent Random Sampling Methods. Statistics and Computing. Springer, Cham. https://doi.org/10.1007/978-3-319-72634-2_2
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