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Typically a number of the initial states are attributed to \"burn in\" and removed, whilst the remainder of the chain is \"thinned\" if compression is also required. In this paper we consider the problem of retrospectively selecting a subset of states, of fixed cardinality, from the sample path such that the approximation provided by their empirical distribution is close to optimal. A novel method is proposed, based on greedy minimisation of a kernel Stein discrepancy, that is suitable for problems where heavy compression is required. Theoretical results guarantee consistency of the method and its effectiveness is demonstrated in the challenging context of parameter inference for ordinary differential equations. Software is available in the Stein Thinning package in Python, R and MATLAB.","url_abs":"https://arxiv.org/abs/2005.03952v5","url_pdf":"https://arxiv.org/pdf/2005.03952v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"optimal-thinning-of-mcmc-output","repo_url":"https://github.com/wilson-ye-chen/stein_thinning","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"optimal-thinning-of-mcmc-output","repo_url":"https://github.com/wilson-ye-chen/stein_thinning_matlab","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"optimal-thinning-of-mcmc-output","repo_url":"https://github.com/wilson-ye-chen/stein.thinning","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2005.03952","atlas_url":"https://app.syntology.ai/?focus=2005.03952","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2005.03952"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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