Change search
ReferencesLink to record
Permanent link

Direct link
Parallel Multiple Proposal MCMC Algorithms
Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, Department of Mathematical Sciences.
2007 (English)MasteroppgaveStudent thesis
Abstract [en]
We explore the variance reduction achievable through parallel implementation of multi-proposal MCMC algorithms and use of control variates. Implemented sequentially multi-proposal MCMC algorithms are of limited value, but they are very well suited for parallelization. Further, discarding the rejected states in an MCMC sampler can intuitively be interpreted as a waste of information. This becomes even more true for a multi-proposal algorithm where we discard several states in each iteration. By creating an alternative estimator consisting of a linear combination of the traditional sample mean and zero mean random variables called control variates we can improve on the traditional estimator. We present a setting for the multi-proposal MCMC algorithm and study it in two examples. The first example considers sampling from a simple Gaussian distribution, while for the second we design the framework for a multi-proposal mode jumping algorithm for sampling from a distribution with several separated modes. We find that the variance reduction achieved from our control variate estimator in general increases as the number of proposals in our sampler increase. For our Gaussian example we find that the benefit from parallelization is small, and that little is gained from increasing the number of proposals. The mode jumping example however is very well suited for parallelization and we get a relative variance reduction pr time of roughly 80% with 16 proposals in each iteration.
Place, publisher, year, edition, pages
Institutt for matematiske fag , 2007. , 40 p.
Keyword [no]
ntnudaim:3425, SIF3 fysikk og matematikk, Industriell matematikk
Identifiers
URN: urn:nbn:no:ntnu:diva-12857Local ID: ntnudaim:3425OAI: oai:DiVA.org:ntnu-12857DiVA: diva2:426895
Supervisors
Available from: 2011-06-27 Created: 2011-06-27

Open Access in DiVA

fulltext(576 kB)857 downloads
File information
File name FULLTEXT01.pdfFile size 576 kBChecksum SHA-512
6dba7188b9fe298592f9c7e02672cb9e05560b7d3c61155253d182e7f6a3a08114ac2c252da332f852d19db76a71ad08ae88de5c9ed42a311afb6c123c08e155
Type fulltextMimetype application/pdf
cover(48 kB)23 downloads
File information
File name COVER01.pdfFile size 48 kBChecksum SHA-512
981e255b20507612268005f0d8348a8687d751fc58cb3bae1d9947352090c2e50ac6a3c4ffc937a501dd1aefa958f1947d66fd9b9e7ebc262395bf50b3b04136
Type coverMimetype application/pdf

By organisation
Department of Mathematical Sciences

Search outside of DiVA

GoogleGoogle Scholar
Total: 857 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 59 hits
ReferencesLink to record
Permanent link

Direct link