{"paper":{"title":"Vertical-likelihood Monte Carlo","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.CO","authors_text":"James G. Scott, Nicholas G. Polson","submitted_at":"2014-09-11T21:24:46Z","abstract_excerpt":"In this review, we address the use of Monte Carlo methods for approximating definite integrals of the form $Z = \\int L(x) d P(x)$, where $L$ is a target function (often a likelihood) and $P$ a finite measure. We present vertical-likelihood Monte Carlo, which is an approach for designing the importance function $g(x)$ used in importance sampling. Our approach exploits a duality between two random variables: the random draw $X \\sim g$, and the corresponding random likelihood ordinate $Y\\equiv L(X)$ of the draw. It is natural to specify $g(x)$ and ask: what is the the implied distribution of $Y$?"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3601","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"}