The Ehresmann connection induced by the Fisher metric on the hierarchical parameter fiber bundle is flat for any smooth posterior, identifying the mixing obstruction as the prior fraction (pooling factor) rather than curvature.
Log-Density Gradient Covariance and Automatic Metric Tensors for Riemannian Manifold Monte Carlo Methods
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A Flat Connection: The Pooling Factor and the Geometry of Centring in Hierarchical MCMC
The Ehresmann connection induced by the Fisher metric on the hierarchical parameter fiber bundle is flat for any smooth posterior, identifying the mixing obstruction as the prior fraction (pooling factor) rather than curvature.