A new arXiv preprint highlights a fundamental identifiability problem in normal-inverse-gamma (NIG) regression, a common tool for evidential deep learning. The authors show that the marginal Student-t likelihood does not uniquely determine the four NIG parameters. Instead, it fixes only three independent combinations, meaning the likelihood is unchanged along a one-dimensional fiber of parameter space. As a result, standard NIG-based uncertainty estimates are not identifiable from data alone.
To address this, the paper proposes PEEL — Physics-Enabled Evidential Learning — which incorporates physical constraints to break the degeneracy. The approach is demonstrated in the context of CT imaging, where reliable and identifiable uncertainty estimates are important for downstream clinical decisions. The authors argue that PEEL resolves the ambiguity while preserving the benefits of evidential learning.
The work is presented as a new announcement on arXiv, and the abstract does not provide quantitative results. No competing claims or alternative methods are discussed in the available text, so the summary reflects only the problem statement and the proposed direction.