Gibbs sampler and coordinate ascent variational inference: A set-theoretical review

One of the fundamental problems in Bayesian statistics is the approximation of the posterior distribution. Gibbs sampler and coordinate ascent variational inference are renownedly utilized approximation techniques that rely on stochastic and deterministic approximations. In this paper, we define fun...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2022-03, Vol.51 (6), p.1549-1568
Main Author: Lee, Se Yoon
Format: Article
Language:English
Subjects:
Approximation
Ascent
Bayesian analysis
coordinate ascent variational inference
duality formula
Gibbs sampler
Mathematical analysis
Statistical inference
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Summary:One of the fundamental problems in Bayesian statistics is the approximation of the posterior distribution. Gibbs sampler and coordinate ascent variational inference are renownedly utilized approximation techniques that rely on stochastic and deterministic approximations. In this paper, we define fundamental sets of densities frequently used in Bayesian inference. We shall be concerned with the clarification of the two schemes from the set-theoretical point of view. This new way provides an alternative mechanism for analyzing the two schemes endowed with pedagogical insights.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2021.1921214