Hierarchical Models and Tuning of Random Walk Metropolis Algorithms
Author
Source
Journal of Probability and Statistics
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-24, 24 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-08-26
Country of Publication
Egypt
No. of Pages
24
Main Subjects
Abstract EN
We obtain weak convergence and optimal scaling results for the random walk Metropolis algorithm with a Gaussian proposal distribution.
The sampler is applied to hierarchical target distributions, which form the building block of many Bayesian analyses.
The global asymptotically optimal proposal variance derived may be computed as a function of the specific target distribution considered.
We also introduce the concept of locally optimal tunings, i.e., tunings that depend on the current position of the Markov chain.
The theorems are proved by studying the generator of the first and second components of the algorithm and verifying their convergence to the generator of a modified RWM algorithm and a diffusion process, respectively.
The rate at which the algorithm explores its state space is optimized by studying the speed measure of the limiting diffusion process.
We illustrate the theory with two examples.
Applications of these results on simulated and real data are also presented.
American Psychological Association (APA)
Bédard, Mylène. 2019. Hierarchical Models and Tuning of Random Walk Metropolis Algorithms. Journal of Probability and Statistics،Vol. 2019, no. 2019, pp.1-24.
https://search.emarefa.net/detail/BIM-1186887
Modern Language Association (MLA)
Bédard, Mylène. Hierarchical Models and Tuning of Random Walk Metropolis Algorithms. Journal of Probability and Statistics No. 2019 (2019), pp.1-24.
https://search.emarefa.net/detail/BIM-1186887
American Medical Association (AMA)
Bédard, Mylène. Hierarchical Models and Tuning of Random Walk Metropolis Algorithms. Journal of Probability and Statistics. 2019. Vol. 2019, no. 2019, pp.1-24.
https://search.emarefa.net/detail/BIM-1186887
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1186887