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.
arXiv preprint arXiv:1910.09407 , year =
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An adaptive hierarchical RMHMC sampler with closed-form leapfrog integrator and automatic mass matrix tuning for efficient MCMC in high-dimensional Bayesian problems.
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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.
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Adaptive Riemannian Manifold Hamiltonian Monte Carlo with Hierarchical Metric
An adaptive hierarchical RMHMC sampler with closed-form leapfrog integrator and automatic mass matrix tuning for efficient MCMC in high-dimensional Bayesian problems.