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December 2014 The containment condition and AdapFail algorithms
Krzysztof Łatuszyński, Jeffrey S. Rosenthal
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J. Appl. Probab. 51(4): 1189-1195 (December 2014).

Abstract

This short note investigates convergence of adaptive Markov chain Monte Carlo algorithms, i.e. algorithms which modify the Markov chain update probabilities on the fly. We focus on the containment condition introduced Roberts and Rosenthal (2007). We show that if the containment condition is not satisfied, then the algorithm will perform very poorly. Specifically, with positive probability, the adaptive algorithm will be asymptotically less efficient then any nonadaptive ergodic MCMC algorithm. We call such algorithms AdapFail, and conclude that they should not be used.

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Krzysztof Łatuszyński. Jeffrey S. Rosenthal. "The containment condition and AdapFail algorithms." J. Appl. Probab. 51 (4) 1189 - 1195, December 2014.

Information

Published: December 2014
First available in Project Euclid: 20 January 2015

zbMATH: 1329.60263
MathSciNet: MR3301296

Subjects:
Primary: 60J05
Secondary: 65C05

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 4 • December 2014
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