My background is computer science. I am fairly new to monte carlo sampling methods and, although I understand the math, I have hard time coming up with intuitive examples for importance sampling. More precisely, could someone provide examples of: - an original distribution one cannot sample from but one can estimate - an importance distribution which can be sampled from and adequate for this original distribution.

Thanks in advance!

My background is computer science. I am fairly new to monte carlo sampling methods and, although I understand the math, I have hard time coming up with intuitive examples for importance sampling. More precisely, could someone provide examples of:

1. an original distribution one cannot sample from but one can estimate
2. an importance distribution which can be sampled from and adequate for this original distribution.