{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T07:31:00Z","timestamp":1773732660838,"version":"3.50.1"},"reference-count":60,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,19]],"date-time":"2021-01-19T00:00:00Z","timestamp":1611014400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PU16-05034"],"award-info":[{"award-number":["PU16-05034"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010198","name":"Ministerio de Econom\u00eda, Industria y Competitividad, Gobierno de Espa\u00f1a","doi-asserted-by":"publisher","award":["MTM2017-86875-C3-1-R"],"award-info":[{"award-number":["MTM2017-86875-C3-1-R"]}],"id":[{"id":"10.13039\/501100010198","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010198","name":"Ministerio de Econom\u00eda, Industria y Competitividad, Gobierno de Espa\u00f1a","doi-asserted-by":"publisher","award":["CEX2019-000904-S"],"award-info":[{"award-number":["CEX2019-000904-S"]}],"id":[{"id":"10.13039\/501100010198","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001961","name":"AXA Research Fund","doi-asserted-by":"publisher","award":["AXA-ICMAT  Chair  in  Adversarial  Risk  Analysis"],"award-info":[{"award-number":["AXA-ICMAT  Chair  in  Adversarial  Risk  Analysis"]}],"id":[{"id":"10.13039\/501100001961","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["MS-1638521"],"award-info":[{"award-number":["MS-1638521"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this work, a framework to boost the efficiency of Bayesian inference in probabilistic models is introduced by embedding a Markov chain sampler within a variational posterior approximation. We call this framework \u201crefined variational approximation\u201d. Its strengths are its ease of implementation and the automatic tuning of sampler parameters, leading to a faster mixing time through automatic differentiation. Several strategies to approximate evidence lower bound (ELBO) computation are also introduced. Its efficient performance is showcased experimentally using state-space models for time-series data, a variational encoder for density estimation and a conditional variational autoencoder as a deep Bayes classifier.<\/jats:p>","DOI":"10.3390\/e23010123","type":"journal-article","created":{"date-parts":[[2021,1,19]],"date-time":"2021-01-19T04:55:31Z","timestamp":1611032131000},"page":"123","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Variationally Inferred Sampling through a Refined Bound"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0349-0714","authenticated-orcid":false,"given":"V\u00edctor","family":"Gallego","sequence":"first","affiliation":[{"name":"Institute of Mathematical Sciences (ICMAT), 28049 Madrid, Spain"},{"name":"Statistical and Applied Mathematical Sciences Institute, Durham, NC 7333, USA"}]},{"given":"David","family":"R\u00edos Insua","sequence":"additional","affiliation":[{"name":"Institute of Mathematical Sciences (ICMAT), 28049 Madrid, Spain"},{"name":"School of Management, University of Shanghai for Science and Technology, Shanghai 201206, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"859","DOI":"10.1080\/01621459.2017.1285773","article-title":"Variational inference: A review for statisticians","volume":"112","author":"Blei","year":"2017","journal-title":"J. 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