Abstract
This paper extends some adaptive schemes that have been developed for the Random Walk Metropolis algorithm to more general versions of the Metropolis-Hastings (MH) algorithm, particularly to the Metropolis Adjusted Langevin algorithm of Roberts and Tweedie (1996). Our simulations show that the adaptation drastically improves the performance of such MH algorithms. We study the convergence of the algorithm. Our proves are based on a new approach to the analysis of stochastic approximation algorithms based on mixingales theory.
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Atchadé, Y.F. An Adaptive Version for the Metropolis Adjusted Langevin Algorithm with a Truncated Drift. Methodol Comput Appl Probab 8, 235–254 (2006). https://doi.org/10.1007/s11009-006-8550-0
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DOI: https://doi.org/10.1007/s11009-006-8550-0
Keywords
- Adaptive Markov Chain Monte Carlo
- Langevin algorithms
- Metropolis-Hastings algorithms
- Stochastic approximation algorithms