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If you have survey data with weights, please use "survey-sampling" instead. If you need to draw Monte Carlo samples from a distribution that is intractable/inconvenient, and have to use a sampler from a simpler distribution that you would then correct with weights, please use "importance-sampling", "monte-carlo" and/or "simulation" instead.
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Practical difference between "sampling" and "re-sampling with replacement"
The practical difference between "sampling" and "sampling with replacement" is really in the accounting part of the probability weights, whether or not you can't have (or don't want) your whole data s …