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Optimal scaling of random walk Metropolis algorithms with discontinuous target densities
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Neal, Peter, Roberts, Gareth O. and Yuen, Wai Kong (2012) Optimal scaling of random walk Metropolis algorithms with discontinuous target densities. Annals of Applied Probability, Volume 22 (Number 5). pp. 1880-1927. doi:10.1214/11-AAP817 ISSN 1050-5164.
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Official URL: http://dx.doi.org/10.1214/11-AAP817
Abstract
We consider the optimal scaling problem for high-dimensional random walk Metropolis (RWM) algorithms where the target distribution has a discontinuous probability density function. Almost all previous analysis has focused upon continuous target densities. The main result is a weak convergence result as the dimensionality d of the target densities converges to ∞. In particular, when the proposal variance is scaled by d−2, the sequence of stochastic processes formed by the first component of each Markov chain converges to an appropriate Langevin diffusion process. Therefore optimizing the efficiency of the RWM algorithm is equivalent to maximizing the speed of the limiting diffusion. This leads to an asymptotic optimal acceptance rate of e−2 (=0.1353) under quite general conditions. The results have major practical implications for the implementation of RWM algorithms by highlighting the detrimental effect of choosing RWM algorithms over Metropolis-within-Gibbs algorithms.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Annals of Applied Probability | ||||
Publisher: | Institute of Mathematical Statistics | ||||
ISSN: | 1050-5164 | ||||
Official Date: | 2012 | ||||
Dates: |
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Volume: | Volume 22 | ||||
Number: | Number 5 | ||||
Page Range: | pp. 1880-1927 | ||||
DOI: | 10.1214/11-AAP817 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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