Title: Not every Gibbs sampler is a special case of the Metropolis–Hastings algorithm
Abstract: It is commonly asserted that the Gibbs sampler is a special case of the Metropolis–Hastings (MH) algorithm. While this statement is true for certain Gibbs samplers, it is not true in general for the version that is taught and used most often, namely, the deterministic scan Gibbs sampler. In this note, I prove that that there exist deterministic scan Gibbs samplers that do not exhibit detailed balance and hence cannot be considered MH samplers. The nuances of various Gibbs sampling schemes are discussed.
Publication Year: 2016
Publication Date: 2016-09-27
Language: en
Type: article
Indexed In: ['crossref']
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