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I'm aware of the Monte Carlo Summation method in discrete spaces, where you can approximate a very long summation over the entire space by a shorter one with only a few randomly selected terms from the original summation (weighted by the inverse probability density of them being chosen).

My question is: should the random selection of summation terms include replacement or not? That is, once one term is selected can it go back into the pool to be selected again? Or, stated yet another way: can one term from the original summation be selected more than once?

If both techniques are possible (with or without replacement), are there any known advantages or disadvantages to each one?

Thank you all,

manuel

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# Question about discrete Monte Carlo Summation

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