{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,13]],"date-time":"2026-08-13T04:29:52Z","timestamp":1786595392378,"version":"build-2736575974"},"reference-count":31,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2026,8,10]],"date-time":"2026-08-10T00:00:00Z","timestamp":1786320000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Approximate transport maps can facilitate exploration of a Bayesian target distribution, but the resulting samples generally do not follow that distribution. To address this problem, we develop residual-slice correction, a sampling framework that combines slice sampling with an approximate transport map held fixed during sampling. Each iteration uses a slice variable to represent the residual left by the map and updates the state while preserving the conditional distribution on the resulting feasible set. To assess sampling efficiency, we derive a lower bound on the corrected chain\u2019s Dirichlet-form gap using a reference Markov kernel. The bound separates movement within each feasible set, the transport\u2013reference comparison, and reference mixing, while projected diagnostics examine the first two factors. Numerical experiments show that residual-slice correction recovers summaries and shape diagnostics distorted by approximate transport; they also show that the choice of Markov update within each feasible set substantially affects mixing efficiency, and that the corrected chains have lower serial dependence after normalizing-flow training. Overall, the framework retains the geometric benefits of approximate transport while preserving the target distribution.<\/jats:p>","DOI":"10.3390\/e28080899","type":"journal-article","created":{"date-parts":[[2026,8,10]],"date-time":"2026-08-10T15:10:24Z","timestamp":1786374624000},"page":"899","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Bayesian Sampling with Approximate Transport Geometry via Residual-Slice Correction"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-7788-2848","authenticated-orcid":false,"given":"Yuanzheng","family":"Zhu","sequence":"first","affiliation":[{"name":"School of Statistics and Data Science, Southwestern University of Finance and Economics, Chengdu 611130, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiao","family":"Hu","sequence":"additional","affiliation":[{"name":"Department of Economics, The Chinese University of Hong Kong, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1063\/1.1699114","article-title":"Equation of State Calculations by Fast Computing Machines","volume":"21","author":"Metropolis","year":"1953","journal-title":"J. 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