The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
Optimal Scaling of Discrete Approximations to Langevin Diffusions
Abstract
Summary: 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.
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Citations
Cites
Monte Carlo sampling methods using Markov chains and their applications.
Hastings, W. K. (1970) · Biometrika · doi:10.1093/biomet/57.1.97 · Cited by 15,195
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Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods
Smith, A. F. M., & Roberts, G. O. (1993) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1993.tb01466.x · Cited by 1,713
Self-citationWeak convergence and optimal scaling of random walk Metropolis algorithms
Roberts, G. O., Gelman, A., & Gilks, W. R. (1997) · The Annals of Applied Probability · doi:10.1214/aoap/1034625254 · Cited by 1,693
Self-citationHuber, P. J. (1997) · Springer Series in Statistics · doi:10.1007/978-1-4612-0667-5_6 · Cited by 1,551
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Grenander, U., & Miller, M. I. (1994) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1994.tb02000.x · Cited by 603
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Cited by
Handbook of Markov Chain Monte Carlo
Brooks, S., Gelman, A., Jones, G., & Meng, X.-L. (2011) · Chapman & Hall/CRC eBooks · doi:10.1201/b10905 · Cited by 2,993
MCMC Using Hamiltonian Dynamics
Neal, R. M. (2011) · Handbook of Markov Chain Monte Carlo · doi:10.1201/b10905-6 · Cited by 2,574
Riemann manifold langevin and hamiltonian monte carlo methods
Girolami, M., & Calderhead, B. (2011) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2010.00765.x · Cited by 1,473
Optimal scaling for various Metropolis-Hastings algorithms
Roberts, G. O., & Rosenthal, J. S. (2001) · Statistical Science · doi:10.1214/ss/1015346320 · Cited by 1,103
Self-citationAndrieu, C., & Thoms, J. (2008) · Statistics and Computing · doi:10.1007/s11222-008-9110-y · Cited by 903
Metadata
- Authors
- Roberts, G. O., & Rosenthal, J. S.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1998-01-01
- Volume
- 60
- Issue
- 1
- Pages
- 255-268
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2029164135
- Cited by
- 632
- References
- 13
- FWCI
- 7.01
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
