Being naïve

From probability theory, we also know the following relationship:

This alone, however, does not help much, since we treat one difficult problem (estimating ) with another one (estimating ).

However, if we naïvely assume that and are independent from each other, simplifies to and we can write it as follows:

Putting everything together, we get the following, quite manageable, formula:

The interesting thing is that although it is not theoretically correct to simply tweak our assumptions when we are in the mood to do so, in this case, it proves to work astonishingly well in real-world applications.

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