Editing Rejection sampling (section)

{{Short description|Computational statistics technique}}
In numerical analysis and [[computational statistics]], '''rejection sampling''' is a basic technique used to generate observations from a [[probability distribution|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 <math>\mathbb{R}^m</math> with a [[Probability density function|density]].

Rejection sampling is based on the observation that to sample a [[random variable]] in one dimension, one can perform a uniformly random sampling of the two-dimensional Cartesian graph, and keep the samples in the region under the graph of its density function.<ref>{{Cite book|title = Generalized Accept-Reject sampling schemes|pages = 342–347|doi = 10.1214/lnms/1196285403|first1 = George|last1 = Casella|first2 = Christian P.|last2 = Robert|first3 = Martin T.|last3 = Wells|isbn = 9780940600614|publisher = Institute of Mathematical Statistics|year = 2004}}</ref><ref name="radford03">{{cite journal
 |first=Radford M. |last=Neal
 |title=Slice Sampling
 |journal=[[Annals of Statistics]]
 |volume=31 |issue=3 |pages=705–767 |year=2003
 |doi=10.1214/aos/1056562461
 |mr=1994729 | zbl = 1051.65007
|doi-access=free}}</ref><ref name="bishop06">{{cite book
  | last = Bishop
  | first = Christopher
  | title = Pattern Recognition and Machine Learning
  | publisher = [[Springer Science+Business Media|Springer]]
  | year = 2006
  | chapter = 11.4: Slice sampling
  | isbn = 978-0-387-31073-2
}}</ref> Note that this property can be extended to ''N''-dimension functions.