Question: In your own words, describe the motivation of importance sampling. A more advanced question is what is the difference between the importance sampling and the optimization of Russian roulette?

dsaksena

Basically we prove here, if our pdf is in proportion to the function f(x), then higher f(x) which contributes more to the pdf has more probability of being sampled in our Monte Carlo integration.

Thus, our integration estimate will be more solid and a better estimate more number of times means the variance (how much much my estimate varies from the truth or more correctly the mean) is lower.

I have to go through Global Illumination, I missed that class, I will add to this comment

Question:In your own words, describe the motivation of importance sampling. A more advanced question is what is the difference between the importance sampling and the optimization of Russian roulette?Basically we prove here, if our pdf is in proportion to the function f(x), then higher f(x) which contributes more to the pdf has more probability of being sampled in our Monte Carlo integration.

Thus, our integration estimate will be more solid and a better estimate more number of times means the variance (how much much my estimate varies from the truth or more correctly the mean) is lower.