Journal of Applied Probability
- J. Appl. Probab.
- Volume 51, Number 4 (2014), 1189-1195.
The containment condition and AdapFail algorithms
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.
J. Appl. Probab., Volume 51, Number 4 (2014), 1189-1195.
First available in Project Euclid: 20 January 2015
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 65C05: Monte Carlo methods
Łatuszyński, Krzysztof; Rosenthal, Jeffrey S. The containment condition and AdapFail algorithms. J. Appl. Probab. 51 (2014), no. 4, 1189--1195. https://projecteuclid.org/euclid.jap/1421763335