Behavior of effective dimension under misspecification and non-Gaussian models

Characterize how the Bayesian effective dimension d_eff(n) = 2 I(Θ; X^{(n)}) / log n behaves in misspecified and non-Gaussian models, and determine whether effective dimension can distinguish between well-specified and poorly specified directions in parameter space.

Background

Most explicit calculations in the paper rely on Gaussian structure. Extending the framework to misspecified or non-Gaussian settings would require controlling mutual information without conjugacy and understanding how identifiability and curvature contribute to d_eff(n).

The authors specifically highlight distinguishing between directions that are well- versus poorly specified as an information-theoretic criterion, which could guide model assessment under misspecification.