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Bayesian Heteroscedastic Regression for Diffusion Tensor Imaging
Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0003-2193-6003
Linköping University, Department of Biomedical Engineering, Division of Biomedical Engineering. Linköping University, Faculty of Science & Engineering. Linköping University, Center for Medical Image Science and Visualization (CMIV).
Linköping University, Department of Computer and Information Science, The Division of Statistics and Machine Learning. Linköping University, Faculty of Arts and Sciences.
2017 (English)In: Modeling, Analysis, and Visualization of Anisotropy / [ed] Thomas Schultz, Evren Özarslan and Ingrid Hotz, Springer Publishing Company, 2017, 1, 257-282 p.Chapter in book (Refereed)
Abstract [en]

We propose a single-diffusion tensor model with heteroscedastic noise and a Bayesian approach via a highly efficient Markov Chain Monte Carlo (MCMC) algorithm for inference. The model is very flexible since both the noise-free signal and the noise variance are functions of diffusion covariates, and the relevant covariates in the noise are automatically selected by Bayesian variable selection. We compare the estimated diffusion tensors from our model to a homoscedastic counterpart with no covariates in the noise, and to commonly used linear and nonlinear least squares methods. The estimated single-diffusion tensors within each voxel are compared with respect to fractional anisotropy (FA) and mean diffusivity (MD). Using data from the Human Connectome Project, our results show that the noise is clearly heteroscedastic, especially the posterior variance for MD is substantially underestimated by the homoscedastic model, and inferences from the homoscedastic model are on average spuriously precise. Inferences from commonly used ordinary and weighted least squares methods (OLS and WLS) show that it is not adequate to estimate the single-diffusion tensor from logarithmic measurements.

Place, publisher, year, edition, pages
Springer Publishing Company, 2017, 1. 257-282 p.
Series
Mathematics and Visualization, ISSN 1612-3786
National Category
Mathematics Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-141878DOI: 10.1007/978-3-319-61358-1_11Scopus ID: 2-s2.0-85031996709ISBN: 978-3-319-61357-4 (print)ISBN: 978-3-319-61358-1 (electronic)OAI: oai:DiVA.org:liu-141878DiVA: diva2:1148542
Conference
Multidisciplinary Approaches to Multivalued Data: Modeling, Visualization, Analysis, April 2016
Funder
Swedish Research Council, 2015-05356Swedish Research Council, 2013-5229
Available from: 2017-10-11 Created: 2017-10-11 Last updated: 2017-12-06Bibliographically approved

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Eklund, Anders

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Wegmann, BertilEklund, AndersVillani, Mattias
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