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In numerical analysis and computational statistics, 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.
Acceptance-Rejection sampling is a way to simulate random samples from an unknown (or difficult to sample from) distribution (called the target distribution) by using random samples from a similar, more convenient probability distribution. A random subset of the generated samples are rejected; the rest are accepted.
We can think of the decision to accept or reject a candidate as a sequence of iid coin flips that has a specific probability of coming up “heads” (i.e. being accepted). That probability is 1 / c1/c and we can calculate that as follows. P(X accepted) = P(U ≤ f(X) cg(X)) = ∫P(U ≤ f(x) cg(x)|X = x)g(x)dx = ∫ f(x) cg(x)g(x)dx = 1 c.
1 Acceptance-Rejection Method As we already know, finding an explicit formula for F−1(y) for the cdf of a rv X we wish to generate, F(x) = P(X ≤ x), is not always possible. Moreover, even if it is, there may be alternative methods for generating a rv distributed as F that is more efficient than the inverse
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The acceptance-rejection method works more efficiently as the distribution of X and Y become similar enough — that is, ρ (x) and its upper bound c are close to one. This makes the rejection region smaller, and so the algorithm is likely to go through fewer repetitions discarding the rejects.
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- 2013-03-22 17:19:20
- 2013-03-22 17:19:20
- acceptance-rejection method
With this Demonstration, you can visualize the rejection sampling technique, which is also known as the acceptance-rejection algorithm. Select a target distribution (the distribution from which you would like to generate random samples) and then choose a "threshold value" that influences the likelihood that a candidate sample from a nontarget ...
Apr 1, 2018 · The accept/reject method, also known as rejection sampling (RS), was suggested by John von Neumann in 1951. It is a classical Monte Carlo technique for universal sampling that can be used to generate samples virtually from any target density p o ( x) by drawing from a simpler proposal density π ( x ).
