Roberts, G. O. and Rosenthal, J. S. (1998) Optimal scaling of discrete approximations to Langevin diffusions. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 60 (1). pp. 255-268. ISSN 1369-7412Full text not available from this repository.
We consider the optimal scaling problem for proposal distributions in Hastings–Metropolis algorithms derived from Langevin diffusions. We prove an asymptotic diffusion limit theorem and show that the relative efficiency of the algorithm can be characterized by its overall acceptance rate, independently of the target distribution. The asymptotically optimal acceptance rate is 0.574. We show that, as a function of dimension n, the complexity of the algorithm is O(n1/3), which compares favourably with the O(n) complexity of random walk Metropolis algorithms. We illustrate this comparison with some example simulations.
|Journal or Publication Title:||Journal of the Royal Statistical Society: Series B (Statistical Methodology)|
|Uncontrolled Keywords:||Hastings–Metropolis algorithm • Langevin algorithm • Markov chain Monte Carlo method • Weak convergence|
|Subjects:||Q Science > QA Mathematics|
|Departments:||Faculty of Science and Technology > Lancaster Environment Centre|
|Deposited On:||14 Nov 2008 16:55|
|Last Modified:||07 Jan 2015 13:12|
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