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The containment condition and AdapFail algorithms
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Łatuszyński, Krzysztof and Rosenthal, Jeffrey S. (Jeffrey Seth) (2014) The containment condition and AdapFail algorithms. Journal of Applied Probability, 51 (4). 1189-1195. doi:10.1239/jap/1421763335 ISSN 0021-9002.
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Official URL: https://doi.org/10.1239/jap/1421763335
Abstract
This short note investigates convergence of adaptive MCMC algorithms, i.e.\ algorithms which modify the Markov chain update probabilities on the fly. We focus on the Containment condition introduced in \cite{roberts2007coupling}. We show that if the Containment condition is \emph{not} satisfied, then the algorithm will perform very poorly. Specifically, with positive probability, the adaptive algorithm will be asymptotically less efficient then \emph{any} nonadaptive ergodic MCMC algorithm. We call such algorithms \texttt{AdapFail}, and conclude that they should not be used.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
Journal or Publication Title: | Journal of Applied Probability | ||||||
Publisher: | Applied Probability Trust | ||||||
ISSN: | 0021-9002 | ||||||
Official Date: | December 2014 | ||||||
Dates: |
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Volume: | 51 | ||||||
Number: | 4 | ||||||
Page Range: | 1189-1195 | ||||||
DOI: | 10.1239/jap/1421763335 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
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