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To tackle this difficulty we explore a Gibbs version of the approximate Bayesian computation approach that runs component-wise approximate Bayesian computation steps aimed at the corresponding conditional posterior distributions, and based on summary statistics of reduced dimensions. While lacking the standard justifications for the Gibbs sampler, the resulting Markov chain is shown to converge in distribution under some partial independence conditions. The associated stationary distribution can further be shown to be close to the true posterior distribution, and some hierarchical versions of the proposed mechanism enjoy a closed-form limiting distribution. Experiments also demonstrate the gain in efficiency brought by the Gibbs version over the standard solution.<\/jats:p>","DOI":"10.1093\/biomet\/asaa090","type":"journal-article","created":{"date-parts":[[2020,10,20]],"date-time":"2020-10-20T19:13:03Z","timestamp":1603221183000},"page":"591-607","source":"Crossref","is-referenced-by-count":26,"title":["Componentwise approximate Bayesian computation via Gibbs-like steps"],"prefix":"10.1093","volume":"108","author":[{"given":"Gr\u00e9goire","family":"Clart\u00e9","sequence":"first","affiliation":[{"name":"CEREMADE, Universit\u00e9 Paris-Dauphine, Place du Mar\u00e9chal de Lattre de Tassigny, 75775 Paris, Cedex 16, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christian P","family":"Robert","sequence":"additional","affiliation":[{"name":"CEREMADE, Universit\u00e9 Paris-Dauphine, Place du Mar\u00e9chal de Lattre de Tassigny, 75775 Paris, Cedex 16, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robin J","family":"Ryder","sequence":"additional","affiliation":[{"name":"CEREMADE, Universit\u00e9 Paris-Dauphine, Place du Mar\u00e9chal de Lattre de Tassigny, 75775 Paris, Cedex 16, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Julien","family":"Stoehr","sequence":"additional","affiliation":[{"name":"CEREMADE, Universit\u00e9 Paris-Dauphine, Place du Mar\u00e9chal de Lattre de Tassigny, 75775 Paris, Cedex 16, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,11,4]]},"reference":[{"key":"2021081218511407600_asaa090-B1","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1080\/01621459.1989.10478750","article-title":"Compatible conditional distributions","volume":"84","author":"Arnold","year":"1989","journal-title":"J. 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