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Not every Gibbs sampler is a special case of the Metropolis–Hastings algorithm

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  • Douglas VanDerwerken

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.

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  • Douglas VanDerwerken, 2017. "Not every Gibbs sampler is a special case of the Metropolis–Hastings algorithm," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(20), pages 10005-10009, October.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:20:p:10005-10009
    DOI: 10.1080/03610926.2016.1228961
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