A Bayesian approach to wavelet-based modelling of discontinuous functions applied to inverse problems. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Aykroyd, Robert G.; Aljohani, Hassan
• Is Part Of: Communications in statistics. Volume 49:Issue 1(2020)
• Page Start: 207
• Page End: 225
• Publication Date: 2020-01-02
• Subjects: Archaeological stratigraphy -- elastic-net -- Haar wavelet -- hierarchical models -- Laplace distribution -- Markov chain Monte Carlo -- sparsity; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2018.1484473
• Languages: English
• ISSNs: 0361-0918

Abstract

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.