{"paper":{"title":"The square root rule for adaptive importance sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.CO","stat.TH"],"primary_cat":"math.ST","authors_text":"Art B. Owen, Yi Zhou","submitted_at":"2019-01-10T00:15:29Z","abstract_excerpt":"In adaptive importance sampling, and other contexts, we have $K>1$ unbiased and uncorrelated estimates $\\hat\\mu_k$ of a common quantity $\\mu$. The optimal unbiased linear combination weights them inversely to their variances but those weights are unknown and hard to estimate. A simple deterministic square root rule based on a working model that $\\mathrm{Var}(\\hat\\mu_k)\\propto k^{-1/2}$ gives an unbisaed estimate of $\\mu$ that is nearly optimal under a wide range of alternative variance patterns. We show that if $\\mathrm{Var}(\\hat\\mu_k)\\propto k^{-y}$ for an unknown rate parameter $y\\in [0,1]$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02976","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}