The Library
On the efficiency of pseudo-marginal random walk Metropolis algorithms
Tools
Sherlock, Chris, Thiéry, Alexandre H., Roberts, Gareth O. and Rosenthal, Jeffrey S. (Jeffrey Seth) (2015) On the efficiency of pseudo-marginal random walk Metropolis algorithms. Annals of statistics, 43 (1). pp. 238-275. doi:10.1214/14-AOS1278 ISSN 0090-5364.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1214/14-AOS1278
Abstract
We examine the behaviour of the pseudo-marginal random walk Metropolis algorithm, where evaluations of the target density for the accept/reject probability are estimated rather than computed precisely. Under relatively general conditions on the target distribution, we obtain limiting formulae for the acceptance rate and for the expected squared jump distance, as the dimension of the target approaches infinity, under the assumption that the noise in the estimate of the log-target is additive and is independent of the position. For targets with independent and identically distributed components, we also obtain a limiting diffusion for the first component.
We then consider the overall efficiency of the algorithm, in terms of both speed of mixing and computational time. Assuming the additive noise is Gaussian and is inversely proportional to the number of unbiased estimates that are used, we prove that the algorithm is optimally efficient when the variance of the noise is approximately 3.3 and the acceptance rate is approximately 7.0%. We also find that the optimal scaling is insensitive to the noise and that the optimal variance of the noise is insensitive to the scaling. The theory is illustrated with a simulation study using the particle marginal random walk Metropolis.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Annals of statistics | ||||
Publisher: | Inst Mathematical Statistics | ||||
ISSN: | 0090-5364 | ||||
Official Date: | 2015 | ||||
Dates: |
|
||||
Volume: | 43 | ||||
Number: | 1 | ||||
Page Range: | pp. 238-275 | ||||
DOI: | 10.1214/14-AOS1278 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |