Statistics and Computing

, Volume 18, Issue 4, pp 343–373

A tutorial on adaptive MCMC


DOI: 10.1007/s11222-008-9110-y

Cite this article as:
Andrieu, C. & Thoms, J. Stat Comput (2008) 18: 343. doi:10.1007/s11222-008-9110-y


We review adaptive Markov chain Monte Carlo algorithms (MCMC) as a mean to optimise their performance. Using simple toy examples we review their theoretical underpinnings, and in particular show why adaptive MCMC algorithms might fail when some fundamental properties are not satisfied. This leads to guidelines concerning the design of correct algorithms. We then review criteria and the useful framework of stochastic approximation, which allows one to systematically optimise generally used criteria, but also analyse the properties of adaptive MCMC algorithms. We then propose a series of novel adaptive algorithms which prove to be robust and reliable in practice. These algorithms are applied to artificial and high dimensional scenarios, but also to the classic mine disaster dataset inference problem.


MCMC Adaptive MCMC Controlled Markov chain Stochastic approximation 

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.School of MathematicsUniversity of BristolBristolUK
  2. 2.Chairs of StatisticsÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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