# adaptive rejection samplingの例文

- For many distributions, this problem can be solved using an adaptive extension ( see adaptive rejection sampling ).
- Various algorithms can be used to choose these individual samples, depending on the exact form of the multivariate distribution : some possibilities are the adaptive rejection sampling methods, the adaptive rejection Metropolis sampling algorithm or its improvements ( see matlab code ), a simple one-dimensional Metropolis Hastings step, or slice sampling.
- However, in the case where the compound distribution is not well-known, it may not be easy to sample from, since it generally will not belong to the exponential family and typically will not be log-concave ( which would make it easy to sample using adaptive rejection sampling, since a closed form always exists ).
- However, in its extended versions ( see below ), it can be considered a general framework for sampling from a large set of variables by sampling each variable ( or in some cases, each group of variables ) in turn, and can incorporate the Metropolis Hastings algorithm ( or more sophisticated methods such as slice sampling, adaptive rejection sampling and adaptive rejection Metropolis algorithms ) to implement one or more of the sampling steps.
- An extension of rejection sampling that can be used to overcome this difficulty and efficiently sample from a wide variety of distributions ( provided that they have log-concave density functions, which is in fact the case for most of the common distributions even those whose " density " functions are "'not "'concave themselves ! ) is known as "'adaptive rejection sampling ( ARS ) " '.