Definition

Let $Y \sim g (y), U \sim u (0, 1)$ be independent random variables, $f (x)$ be a PDF which we want to sample, and $M 0, \frac{f ( x )}{g ( x )} \leq M$ step 1: Generate $Y$ and $U \sim u (0, 1)$ . step 2: If $U \leq \frac{f ( y )}{M g ( y )} \Rightarrow X := Y$ otherwise, go to step 1. step 3. repeat step 1 and 2.