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Bayesian Nonparametric Scalar-on-Image Regression via Potts-Gibbs Random Partition Models

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New Frontiers in Bayesian Statistics (BAYSM 2021)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 405))

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Abstract

Scalar-on-image regression aims to investigate changes in a scalar response of interest based on high-dimensional imaging data. We propose a novel Bayesian nonparametric scalar-on-image regression model that utilises the spatial coordinates of the voxels to group voxels with similar effects on the response to have a common coefficient. We employ the Potts-Gibbs random partition model as the prior for the random partition in which the partition process is spatially dependent, thereby encouraging groups representing spatially contiguous regions. In addition, Bayesian shrinkage priors are utilised to identify the covariates and regions that are most relevant for the prediction. The proposed model is illustrated using the simulated data sets.

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Authors and Affiliations

  1. School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh James Clerk Maxwell Building, Edinburgh, UK

    Mica Shu Xian Teo & Sara Wade

Authors
  1. Mica Shu Xian Teo
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  2. Sara Wade
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Correspondence to Sara Wade .

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Editors and Affiliations

  1. Dipartimento di Scienze Economiche, Università degli Studi di Bergamo, Bergamo, Italy

    Raffaele Argiento

  2. Department of Economics, Management and Statistics, University of Milano-Bicocca, Milan, Italy

    Federico Camerlenghi

  3. Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, MA, USA

    Sally Paganin

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Teo, M.S.X., Wade, S. (2022). Bayesian Nonparametric Scalar-on-Image Regression via Potts-Gibbs Random Partition Models. In: Argiento, R., Camerlenghi, F., Paganin, S. (eds) New Frontiers in Bayesian Statistics. BAYSM 2021. Springer Proceedings in Mathematics & Statistics, vol 405. Springer, Cham. https://doi.org/10.1007/978-3-031-16427-9_5

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