Bayesian registration of functions and curves
Bayesian analysis of functions and curves is considered, where warping and other geometrical transformations are often required for meaningful comparisons. The functions and curves of interest are represented using the recently introduced square root velocity function, which enables a warping invar...
| Main Authors: | , , |
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| Format: | Article |
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International Society for Bayesian Analysis
2015
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| Online Access: | https://eprints.nottingham.ac.uk/29193/ |
| _version_ | 1848793733788598272 |
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| author | Cheng, Wen Dryden, Ian L. Huang, Xianzheng |
| author_facet | Cheng, Wen Dryden, Ian L. Huang, Xianzheng |
| author_sort | Cheng, Wen |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Bayesian analysis of functions and curves is considered, where warping and other geometrical transformations are often required for meaningful comparisons. The functions and curves of interest are represented using the recently introduced square root velocity function, which enables a warping invariant elastic distance to be calculated in a straightforward manner. We distinguish between various spaces of interest: the original space, the ambient space after standardizing, and the quotient space after removing a group of transformations. Using Gaussian process models in the ambient space and Dirichlet priors for the warping functions, we explore Bayesian inference for curves and functions. Markov chain Monte Carlo algorithms are introduced for simulating from the posterior. We also compare ambient and quotient space estimators for mean shape, and explain their frequent similarity in many practical problems using a Laplace approximation. Simulation studies are carried out, as well as practical alignment of growth rate functions and shape classification of mouse vertebra outlines in evolutionary biology. We also compare the performance of our Bayesian method with some alternative approaches. |
| first_indexed | 2025-11-14T19:05:00Z |
| format | Article |
| id | nottingham-29193 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:05:00Z |
| publishDate | 2015 |
| publisher | International Society for Bayesian Analysis |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-291932020-05-04T20:10:43Z https://eprints.nottingham.ac.uk/29193/ Bayesian registration of functions and curves Cheng, Wen Dryden, Ian L. Huang, Xianzheng Bayesian analysis of functions and curves is considered, where warping and other geometrical transformations are often required for meaningful comparisons. The functions and curves of interest are represented using the recently introduced square root velocity function, which enables a warping invariant elastic distance to be calculated in a straightforward manner. We distinguish between various spaces of interest: the original space, the ambient space after standardizing, and the quotient space after removing a group of transformations. Using Gaussian process models in the ambient space and Dirichlet priors for the warping functions, we explore Bayesian inference for curves and functions. Markov chain Monte Carlo algorithms are introduced for simulating from the posterior. We also compare ambient and quotient space estimators for mean shape, and explain their frequent similarity in many practical problems using a Laplace approximation. Simulation studies are carried out, as well as practical alignment of growth rate functions and shape classification of mouse vertebra outlines in evolutionary biology. We also compare the performance of our Bayesian method with some alternative approaches. International Society for Bayesian Analysis 2015 Article PeerReviewed Cheng, Wen, Dryden, Ian L. and Huang, Xianzheng (2015) Bayesian registration of functions and curves. Bayesian Analysis, 2015 . ISSN 1936-0975 Ambient space Dirichlet Gaussian process Quotient space Shape Warp. http://projecteuclid.org/euclid.ba/1433162661 doi:10.1214/15-BA957 doi:10.1214/15-BA957 |
| spellingShingle | Ambient space Dirichlet Gaussian process Quotient space Shape Warp. Cheng, Wen Dryden, Ian L. Huang, Xianzheng Bayesian registration of functions and curves |
| title | Bayesian registration of functions and curves |
| title_full | Bayesian registration of functions and curves |
| title_fullStr | Bayesian registration of functions and curves |
| title_full_unstemmed | Bayesian registration of functions and curves |
| title_short | Bayesian registration of functions and curves |
| title_sort | bayesian registration of functions and curves |
| topic | Ambient space Dirichlet Gaussian process Quotient space Shape Warp. |
| url | https://eprints.nottingham.ac.uk/29193/ https://eprints.nottingham.ac.uk/29193/ https://eprints.nottingham.ac.uk/29193/ |