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Published in:
2009 | OriginalPaper | Chapter
Computational Complexity of Metropolis-Hastings Methods in High Dimensions
Authors : Alexandros Beskos, Andrew Stuart
Published in: Monte Carlo and Quasi-Monte Carlo Methods 2008
Publisher: Springer Berlin Heidelberg
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This article contains an overview of the literature concerning the computational complexity of Metropolis-Hastings based MCMC methods for sampling probability measures on ℝ
d
, when the dimension
d
is large. The material is structured in three parts addressing, in turn, the following questions: (i) what are sensible assumptions to make on the family of probability measures indexed by
d
? (ii) what is known concerning computational complexity for Metropolis-Hastings methods applied to these families? (iii) what remains open in this area?