Folded Transport MCMC: Certifiable Quotient Posterior Computation for Symmetric Bayesian Models

• URL: http://arxiv.org/abs/2606.04307v1
• Date: Wed, 03 Jun 2026 00:26:46 GMT
• Title: Folded Transport MCMC: Certifiable Quotient Posterior Computation for Symmetric Bayesian Models
• Abstract summary: We introduce Folded Transport MCMC, which performs inference directly on the quotient posterior.<n>On real accelerometer data from a supertall building during Typhoon Mangkhut, FolT-MCMC yields a non-vacuous quantile-core certificate.
• Score: 3.8549131582427303
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Bayesian models with finite symmetry - mixture models with exchangeable components, structural identification with closely-spaced modes - define posteriors that are invariant under a group of label permutations, creating redundant multimodality that degrades MCMC convergence diagnostics. We introduce Folded Transport MCMC (FolT-MCMC), which performs inference directly on the quotient posterior by constructing an independence sampler on the fundamental domain of the symmetry group. The quotient proposal is formed by symmetrising a learned normalising flow over the group orbits. We prove that the LCNF oscillation-based certification framework transfers to the quotient metric with a stabiliser-corrected ball-mass bound and improved covering radius, and that the quantile-core certified lower bound improves whenever the unfolded flow exhibits cross-mode proposal deficiency. On Gaussian mixtures (d = 2 - 20), label-switching targets (up to 24 equivalent modes), and a standard Bayesian three-component mixture posterior, the quantile-core certified improvement ratio ranges from 2x to 145x, with the folded certificate empirically nearly dimension-free. On real accelerometer data from a supertall building during Typhoon Mangkhut, FolT-MCMC yields a non-vacuous quantile-core certificate where the unfolded certificate is vacuous.

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