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We show that many recently introduced algorithms, such as the locally informed sampler of Zanella (J Am Stat Assoc 115(530):852\u2013865, 2020), the locally informed with thresholded proposal of Zhou et al. (Dimension-free mixing for high-dimensional Bayesian variable selection, 2021) and the adaptively scaled individual adaptation sampler of Griffin et al. (Biometrika 108(1):53\u201369, 2021), can be viewed as particular cases within the framework. We then describe a novel algorithm, the<jats:italic>adaptive random neighbourhood informed<\/jats:italic>sampler, which combines ideas from these existing approaches. We show using several examples of both real and simulated data-sets that a computationally efficient point-wise implementation (PARNI) provides more reliable inferences on a range of variable selection problems, particularly in the very large<jats:italic>p<\/jats:italic>setting.<\/jats:p>","DOI":"10.1007\/s11222-022-10137-8","type":"journal-article","created":{"date-parts":[[2022,9,30]],"date-time":"2022-09-30T18:04:37Z","timestamp":1664561077000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Adaptive random neighbourhood informed Markov chain Monte Carlo for high-dimensional Bayesian variable selection"],"prefix":"10.1007","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2434-1841","authenticated-orcid":false,"given":"Xitong","family":"Liang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Samuel","family":"Livingstone","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jim","family":"Griffin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,9,30]]},"reference":[{"key":"10137_CR1","unstructured":"Andrieu, C., Lee, A., Livingstone, S.: A general perspective on the Metropolis\u2013Hastings kernel. arXiv:2012.14881 (2020)"},{"issue":"4","key":"10137_CR2","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1007\/s11222-008-9110-y","volume":"18","author":"C Andrieu","year":"2008","unstructured":"Andrieu, C., Thoms, J.: A tutorial on adaptive MCMC. 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