Rejection sampling Guide, Meaning , Facts, Information and Description
For sampling values from an arbitrary probability distribution function by using an instrumental distribution under the only restriction that where is an appropriate bound on . The algorithm goes as follows: sample from and from and check whether or not . If this holds, accept as a realization of ; if not, reject the value of and repeat the sampling step.The validation of this method is the envelope principle: when simulating the pair , one produces a uniform simulation over the subgraph of . Accepting only pairs such that then produces pairs uniformly distributed over the subgraph of and thus, marginaly, a simulation from .
Also called the acceptance-rejection method or "accept-reject algorithm", this method relates to the general field of Monte Carlo techniques, including Markov chain Monte Carlo algorithms that also use a proxy distribution to achieve simulation from the target distribution .