Question

Approaches to reduce rejection of numbers in sampling statistics

Answer 1

In numerical analysis, rejection sampling is a basic technique used to generate observations from a distribution. It is also commonly called the acceptance-rejection method or "accept-reject algorithm" and is a type of exact simulation method. The method works for any distribution in {\displaystyle \mathbb {R} ^{m}} with a density.

Rejection sampling is based on the observation that to sample a random variableone can perform a uniformly random sampling of the 2D cartesian graph, and keep the samples in the region under the graph of its density function. Note that this property can be extended to N-dimension functions.