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Creating samples from a well-specified population using a probabilistic method and/or producing random numbers from a specified distribution. As this tag is ambiguous, please consider [survey-sampling] for the former and [monte-carlo] or [simulation] for the latter. For questions regarding creating random samples from known distributions, please consider using the [random-generation] tag.
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Sampling according to a product of a known density and a probability function
However, I'd like to use $q(x)$ as a proposal density in the context of importance sampling to generate samples that are rare under $p$. … So, this rejection sampling approach would be very inefficient and essentially defeat the purpose of using importance sampling. …