Aykroyd, RG orcid.org/0000-0003-3700-0816 and Aljohani, H (2020) A Bayesian approach to wavelet-based modelling of discontinuous functions applied to inverse problems. Communications in Statistics - Simulation and Computation, 49 (1). pp. 207-225. ISSN 0361-0918
Abstract
Inverse problems are examples of regression with more unknowns than the amount of information in the data and hence constraints are imposed through prior information. The proposed method defines the underlying function as a wavelet approximation which is related to the data through a convolution. The wavelets provide a sparse and multi-resolution solution which can capture local behaviour in an adaptive way. Varied prior models are considered along with level-specific prior parameter estimation. Archaeological stratigraphy data are considered where vertical earth cores are analysed producing clear piecewise constant function estimates.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2018 Taylor & Francis Group, LLC. This is an author produced version of a paper published in Communications in Statistics - Simulation and Computation. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Archaeological stratigraphy, elastic-net, Haar wavelet, hierarchical models, Laplace distribution, Markov chain Monte Carlo, sparsity |
Dates: |
|
Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 15 May 2018 15:23 |
Last Modified: | 29 Jan 2020 16:07 |
Status: | Published |
Publisher: | Taylor & Francis |
Identification Number: | 10.1080/03610918.2018.1484473 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:130812 |