Editing Rejection sampling (section)

==Drawbacks==

Rejection sampling requires knowing the target distribution (specifically, ability to evaluate target PDF at any point).

Rejection sampling can lead to a lot of unwanted samples being taken if the function being sampled is highly concentrated in a certain region, for example a function that has a spike at some location.  For many distributions, this problem can be solved using an adaptive extension (see [[#Adaptive rejection sampling|adaptive rejection sampling]]), or with an appropriate change of variables with the method of the [[ratio of uniforms]]. In addition, as the dimensions of the problem get larger, the ratio of the embedded volume to the "corners" of the embedding volume tends towards zero, thus a lot of rejections can take place before a useful sample is generated, thus making the algorithm inefficient and impractical. See [[curse of dimensionality]]. In high dimensions, it is necessary to use a different approach, typically a Markov chain Monte Carlo method such as [[Metropolis sampling]] or [[Gibbs sampling]]. (However, Gibbs sampling, which breaks down a multi-dimensional sampling problem into a series of low-dimensional samples, may use rejection sampling as one of its steps.)