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Bayesian linear size-and-shape regression with applications to face data

Dryden, Ian L.; Le, Huiling; Kim, Kwang-Rae

Authors

IAN DRYDEN IAN.DRYDEN@NOTTINGHAM.AC.UK
Professor of Statistics

HUILING LE huiling.le@nottingham.ac.uk
Professor of Probability

Kwang-Rae Kim



Abstract

Regression models for size-and-shape analysis are developed, where the model is specified in the Euclidean space of the landmark coordinates. Statistical models in this space (which is known as the top space or ambient space) are often easier for practitioners to understand than alternative models in the quotient space of size-and-shapes. We consider a Bayesian linear size-and-shape regression model in which the response variable is given by labelled configuration matrix, and the covariates represent quantities such as gender and age. It is important to parameterize the model so that it is identifiable, and we use the LQ decomposition in the intercept term in the model for this purpose. Gamma priors for the inverse variance of the error term, matrix Fisher priors for the random rotation matrix, and flat priors for the regression coefficients are used. Markov chain Monte Carlo algorithms are used for sampling from the posterior distribution, in particular by using combinations of Metropolis-Hastings updates and a Gibbs sampler.The proposed Bayesian methodology is illustrated with an application to forensic facial data in three dimensions, where we investigate the main changes in growth by describing relative movements of landmarks for each gender over time.

Citation

Dryden, I. L., Le, H., & Kim, K. (2019). Bayesian linear size-and-shape regression with applications to face data. Sankhya A, 81(1), 83–103. https://doi.org/10.1007/s13171-018-0136-8

Journal Article Type Article
Acceptance Date Jun 20, 2018
Online Publication Date Aug 29, 2018
Publication Date 2019-02
Deposit Date Jul 17, 2018
Publicly Available Date Aug 30, 2019
Journal Sankhya A
Print ISSN 0972-7671
Electronic ISSN 0972-7671
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 81
Issue 1
Pages 83–103
DOI https://doi.org/10.1007/s13171-018-0136-8
Public URL http://eprints.nottingham.ac.uk/id/eprint/52985
Publisher URL https://link.springer.com/article/10.1007/s13171-018-0136-8
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/





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