What if the shadow in real life is due to some bad variance in the computer simulating this world

Would we ever want to increase variance?

We look at the average (first moment) and variance (second moment), but do we ever care about higher moments when rendering?

Would we have to adjust the variance based on the image we are trying to produce? Or can we assume that a lower variance is always desired?

What are some cases where a noisy image would be preferred?