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This routinely occurs when there are aspects of the target distribution that are not well captured by the approximating distribution, in which case more stable estimates can be obtained by modifying extreme importance ratios. We present a new method for stabilizing importance weights using a generalized Pareto distribution fit to the upper tail of the distribution of the simulated importance ratios. The method, which empirically performs better than existing methods for stabilizing importance sampling estimates, includes stabilized effective sample size estimates, Monte Carlo error estimates, and convergence diagnostics. The presented Pareto $\\hat{k}$ finite sample convergence rate diagnostic is useful for any Monte Carlo estimator.","url_abs":"https://arxiv.org/abs/1507.02646v9","url_pdf":"https://arxiv.org/pdf/1507.02646v9.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":"pareto-smoothed-importance-sampling","repo_url":"https://github.com/avehtari/PSIS","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"pareto-smoothed-importance-sampling","repo_url":"https://github.com/stan-dev/loo","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"pareto-smoothed-importance-sampling","repo_url":"https://github.com/CoryMcCartan/adjustr","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"pareto-smoothed-importance-sampling","repo_url":"https://github.com/StatisticalRethinkingJulia/ModelComparisons.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}},{"paper_slug":"pareto-smoothed-importance-sampling","repo_url":"https://github.com/StatisticalRethinkingJulia/ParetoSmoothedImportanceSampling.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}},{"paper_slug":"pareto-smoothed-importance-sampling","repo_url":"https://github.com/StatisticalRethinkingJulia/StatsModelComparisons.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}},{"paper_slug":"pareto-smoothed-importance-sampling","repo_url":"https://github.com/arviz-devs/PSIS.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"pareto-smoothed-importance-sampling","repo_url":"https://github.com/jgabry/loo","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}},{"paper_slug":"pareto-smoothed-importance-sampling","repo_url":"https://github.com/n-kall/priorsense","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}}],"tasks":[{"task_slug":"diagnostic","task_name":"Diagnostic"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1507.02646","atlas_url":"https://app.syntology.ai/?focus=1507.02646","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1507.02646"}},"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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