{"paper":{"title":"When is it best to follow the leader?","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"L.C.G. Rogers, Philip Ernst, Quan Zhou","submitted_at":"2018-04-16T02:23:46Z","abstract_excerpt":"An object is hidden in one of $N$ boxes. Initially, the probability that it is in box $i$ is $\\pi_i(0)$. You then search in continuous time, observing box $J_t$ at time $t$, and receiving a signal as you observe: if the box you are observing does not contain the object, your signal is a Brownian motion, but if it does contain the object your signal is a Brownian motion with positive drift $\\mu$. It is straightforward to derive the evolution of the posterior distribution $\\pi(t)$ for the location of the object. If $T$ denotes the first time that one of the $\\pi_j(t)$ reaches a desired threshold"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05479","kind":"arxiv","version":1},"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"}