Show simple item record

dc.contributor.authorDuffield, Samuel
dc.date.accessioned2022-04-01T13:09:26Z
dc.date.available2022-04-01T13:09:26Z
dc.date.submitted2021-09-06
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/335667
dc.description.abstractThe common theme of this thesis is the concept of using Monte Carlo techniques to approximate a sequence of probability distributions. Novel methodological contributions are found in Chapter 3 through to Chapter 6. In Chapter 3 we derive a method for the complete characterisation of online statistical models where Monte Carlo approximations are defined sequentially as new data arrive. We then demonstrate the utility of this method in Chapter 4 for the compelling application of de-noising sequential GPS coordinates to be restricted to a road network. In Chapter 5 and Chapter 6, the sequence of probability distributions are defined artificially in order to gradually (and more effectively) approach a single offline target probability distribution. Chapter 5 adopts ideas from high-dimensional time series to efficiently tackle the difficult setting where we cannot evaluate the density of the target distribution and instead can only generate synthetic data. Chapter 6 explores the use of a scalable Hessian approximation in the more common scenario where the target density can be evaluated and even differentiated. Finally, Chapter 7 describes a general purpose software package that can be used to implement and customise all of the discussed algorithms at competitive speeds.
dc.description.sponsorshipEPSRC
dc.rightsAttribution-NonCommercial 4.0 International (CC BY-NC 4.0)
dc.rights.urihttps://creativecommons.org/licenses/by-nc/4.0/
dc.subjectBayesian inference
dc.subjectMonte Carlo
dc.subjectState-space Models
dc.subjectStatistics
dc.titleIterative Monte Carlo Approximations for Bayesian Inference
dc.typeThesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnameDoctor of Philosophy (PhD)
dc.publisher.institutionUniversity of Cambridge
dc.date.updated2022-03-25T16:53:20Z
dc.identifier.doi10.17863/CAM.83098
rioxxterms.licenseref.urihttps://creativecommons.org/licenses/by-nc/4.0/
rioxxterms.typeThesis
dc.publisher.collegeSt Edmunds
pubs.funder-project-idEPSRC (1890282)
pubs.funder-project-idEngineering and Physical Sciences Research Council (1890282)
cam.supervisorSingh, Sumeetpal
datacite.issupplementedby.doiPredicting Taxi Passenger Demand Using Streaming Data
datacite.issupplementedby.doiPhilatelic Mixtures and Multimodal Densities
cam.depositDate2022-03-25
pubs.licence-identifierapollo-deposit-licence-2-1
pubs.licence-display-nameApollo Repository Deposit Licence Agreement


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record

Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)
Except where otherwise noted, this item's licence is described as Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)