If we use importance sampling, won't the integral always be underestimated?
joshua16266261
I don't think the integral will be underestimated, because in the slide that proved that the Monte Carlo estimate is unbiased, it used an arbitrary PDF. For importance sampling, I think we are just changing the PDF that we draw points from (to be nonuniform), but we don't actually change the formula for the Monte Carlo estimate, so the proof should still hold.
If we use importance sampling, won't the integral always be underestimated?
I don't think the integral will be underestimated, because in the slide that proved that the Monte Carlo estimate is unbiased, it used an arbitrary PDF. For importance sampling, I think we are just changing the PDF that we draw points from (to be nonuniform), but we don't actually change the formula for the Monte Carlo estimate, so the proof should still hold.