IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v103y2019i3d10.1007_s10182-018-00334-0.html
   My bibliography  Save this article

Approximate large-scale Bayesian spatial modeling with application to quantitative magnetic resonance imaging

Author

Listed:
  • Selma Metzner

    (Physikalisch–Technische Bundesanstalt)

  • Gerd Wübbeler

    (Physikalisch–Technische Bundesanstalt)

  • Clemens Elster

    (Physikalisch–Technische Bundesanstalt)

Abstract

We consider the Bayesian inference of nonlinear, large-scale regression problems in which the parameters model the spatial distribution of some property. A homoscedastic Gaussian sampling distribution is supposed as well as certain assumptions about the regression function. Propriety of the posterior and the existence of its moments are explored when using improper prior distributions expressing different levels of prior knowledge, ranging from a purely noninformative prior over intrinsic Gaussian Markov random field priors to a partition prior. The considered class of problems includes magnetic resonance fingerprinting (MRF). We apply an approximate Bayesian inference to this particular application and demonstrate its practicability in dimensions up to $$10^5$$ 10 5 or larger. The benefit of incorporating substantial prior knowledge is illustrated. By analyzing simulated realistic MRF data, it is shown that MAP estimates can significantly improve the results achieved with maximum likelihood estimation.

Suggested Citation

  • Selma Metzner & Gerd Wübbeler & Clemens Elster, 2019. "Approximate large-scale Bayesian spatial modeling with application to quantitative magnetic resonance imaging," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 333-355, September.
    • Handle: RePEc:spr:alstar:v:103:y:2019:i:3:d:10.1007_s10182-018-00334-0
    DOI: 10.1007/s10182-018-00334-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10182-018-00334-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10182-018-00334-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. David M. Blei & Alp Kucukelbir & Jon D. McAuliffe, 2017. "Variational Inference: A Review for Statisticians," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 859-877, April.
    2. Nishii, Ryuei & Eguchi, Shinto, 2006. "Image classification based on Markov random field models with Jeffreys divergence," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 1997-2008, October.
    3. Clemens Elster & Gerd Wübbeler, 2017. "Bayesian inference using a noninformative prior for linear Gaussian random coefficient regression with inhomogeneous within-class variances," Computational Statistics, Springer, vol. 32(1), pages 51-69, March.
    4. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    5. Smith, Michael & Fahrmeir, Ludwig, 2007. "Spatial Bayesian Variable Selection With Application to Functional Magnetic Resonance Imaging," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 417-431, June.
    6. Dan Ma & Vikas Gulani & Nicole Seiberlich & Kecheng Liu & Jeffrey L. Sunshine & Jeffrey L. Duerk & Mark A. Griswold, 2013. "Magnetic resonance fingerprinting," Nature, Nature, vol. 495(7440), pages 187-192, March.
    7. Garthwaite, Paul H. & Kadane, Joseph B. & O'Hagan, Anthony, 2005. "Statistical Methods for Eliciting Probability Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 680-701, June.
    8. Paul Schmidt & Volker J Schmid & Christian Gaser & Dorothea Buck & Susanne Bührlen & Annette Förschler & Mark Mühlau, 2013. "Fully Bayesian Inference for Structural MRI: Application to Segmentation and Statistical Analysis of T2-Hypointensities," PLOS ONE, Public Library of Science, vol. 8(7), pages 1-14, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    2. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business Statistics.
    3. Jeong Hwan Kook & Michele Guindani & Linlin Zhang & Marina Vannucci, 2019. "NPBayes-fMRI: Non-parametric Bayesian General Linear Models for Single- and Multi-Subject fMRI Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(1), pages 3-21, April.
    4. Linda S. L. Tan, 2021. "Use of model reparametrization to improve variational Bayes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(1), pages 30-57, February.
    5. Gael M. Martin & David T. Frazier & Christian P. Robert, 2021. "Approximating Bayes in the 21st Century," Monash Econometrics and Business Statistics Working Papers 24/21, Monash University, Department of Econometrics and Business Statistics.
    6. Murphy, James, 2020. "Explanatory Item Response Models for Dyadic Data from Multiple Groups," SocArXiv sx9um, Center for Open Science.
    7. Matias Quiroz & Mattias Villani & Robert Kohn & Minh-Ngoc Tran & Khue-Dung Dang, 2018. "Subsampling MCMC - an Introduction for the Survey Statistician," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 33-69, December.
    8. Dang, Khue-Dung & Quiroz, Matias & Kohn, Robert & Tran, Minh-Ngoc & Villani, Mattias, 2019. "Hamiltonian Monte Carlo with Energy Conserving Subsampling," Working Paper Series 372, Sveriges Riksbank (Central Bank of Sweden).
    9. Martin, Gael M. & Frazier, David T. & Maneesoonthorn, Worapree & Loaiza-Maya, Rubén & Huber, Florian & Koop, Gary & Maheu, John & Nibbering, Didier & Panagiotelis, Anastasios, 2024. "Bayesian forecasting in economics and finance: A modern review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 811-839.
    10. Jiayuan Dong & Jiankan Liao & Xun Huan & Daniel Cooper, 2023. "Expert elicitation and data noise learning for material flow analysis using Bayesian inference," Journal of Industrial Ecology, Yale University, vol. 27(4), pages 1105-1122, August.
    11. Gael M. Martin & David T. Frazier & Christian P. Robert, 2022. "Computing Bayes: From Then `Til Now," Monash Econometrics and Business Statistics Working Papers 14/22, Monash University, Department of Econometrics and Business Statistics.
    12. Schmidt, Paul & Mühlau, Mark & Schmid, Volker, 2017. "Fitting large-scale structured additive regression models using Krylov subspace methods," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 59-75.
    13. Nikoline N. Knudsen & Jörg Schullehner & Birgitte Hansen & Lisbeth F. Jørgensen & Søren M. Kristiansen & Denitza D. Voutchkova & Thomas A. Gerds & Per K. Andersen & Kristine Bihrmann & Morten Grønbæk , 2017. "Lithium in Drinking Water and Incidence of Suicide: A Nationwide Individual-Level Cohort Study with 22 Years of Follow-Up," IJERPH, MDPI, vol. 14(6), pages 1-13, June.
    14. Maarten Ijzerman & Lotte Steuten, 2011. "Early assessment of medical technologies to inform product development and market access," Applied Health Economics and Health Policy, Springer, vol. 9(5), pages 331-347, September.
    15. Leonardo Padilla & Bernado Lagos‐Álvarez & Jorge Mateu & Emilio Porcu, 2020. "Space‐time autoregressive estimation and prediction with missing data based on Kalman filtering," Environmetrics, John Wiley & Sons, Ltd., vol. 31(7), November.
    16. Scott, Ryan P. & Scott, Tyler A., 2019. "Investing in collaboration for safety: Assessing grants to states for oil and gas distribution pipeline safety program enhancement," Energy Policy, Elsevier, vol. 124(C), pages 332-345.
    17. Cho, Daegon & Hwang, Youngdeok & Park, Jongwon, 2018. "More buzz, more vibes: Impact of social media on concert distribution," Journal of Economic Behavior & Organization, Elsevier, vol. 156(C), pages 103-113.
    18. Claire Copeland & Britta Turner & Gareth Powells & Kevin Wilson, 2022. "In Search of Complementarity: Insights from an Exercise in Quantifying Qualitative Energy Futures," Energies, MDPI, vol. 15(15), pages 1-21, July.
    19. Shen Liu & Hongyan Liu, 2021. "Tagging Items Automatically Based on Both Content Information and Browsing Behaviors," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 882-897, July.
    20. Brown, Paul T. & Joshi, Chaitanya & Joe, Stephen & Rue, Håvard, 2021. "A novel method of marginalisation using low discrepancy sequences for integrated nested Laplace approximations," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:alstar:v:103:y:2019:i:3:d:10.1007_s10182-018-00334-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.