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Edited: I have been researching about density function estimation from a sample of data, and I noticed that there are a lot of researches the estimate the density with the normalizing factor and others that don't.

What are the real world applications of knowing the normalizing constant of the density?

I noticed that if we just want to rank the data by density we don't really need the factor as it is a constant, except for the mathematical meaning that the integral of the density should equal to 1, what else is good about knowing it?

Lazag
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  • I marked it as a duplicate of another thread that while is titled differently, answers your question in detail. TL;DR your understanding is correct, we need the constant when we care about the probability densities themselves, when we need it to be a proper probability distribution that integrates to one, but for optimization, random generation, etc it is not needed. – Tim Sep 28 '22 at 07:33
  • @Tim , Thank you, so for density estimation it is irrelevant to search for it because there are no real world applications of knowing the constant? – Lazag Sep 28 '22 at 12:54
  • It depends what you are using the estimated densities for. – Tim Sep 28 '22 at 12:57
  • @Tim I think I should have reformulated my question to what are the real world applications of knowing the normalizing constant of the density. Do you happen to know any? – Lazag Sep 28 '22 at 12:58
  • If you want to do any math on the densities, you need them to be normalized. – Tim Sep 28 '22 at 13:12

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