Importance sampling is a variance reduction methods technique for Monte Carlo methods. The idea is to put more samples where the PDF is bigger.

importance sampling.png

Process of Importance Sampling

  1. Having an integral over the domain
  2. Pick a PDF that is non-zero over the domain
  3. We average a bunch of where is a random number with PDF

Any choice of PDF will converge to the correct anwser eventually, but the closer the PDF approximate , the faster we converge.

References