Bayesian nonparametric scalar-on-image regression via Potts-Gibbs random partition models

TL;DR

This paper introduces a Bayesian nonparametric model for scalar-on-image regression that leverages spatial information to identify contiguous regions influencing the response, improving interpretability and prediction accuracy.

Contribution

It develops a novel Potts-Gibbs random partition prior that encourages spatially contiguous grouping of voxels, enhancing region detection in imaging data.

Findings

Effective in simulated data for identifying relevant regions.

Encourages spatially contiguous voxel grouping.

Improves interpretability of scalar-on-image relationships.

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.