{"paper":{"title":"Recursive computation for evaluating the exact $p$-values of temporal and spatial scan statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME"],"primary_cat":"stat.CO","authors_text":"Hisayuki Hara, Kunihiko Takahashi, Satoshi Kuriki","submitted_at":"2015-10-31T10:36:41Z","abstract_excerpt":"Let $V$ be a finite set of indices, and let $B_i$, $i=1,\\ldots,m$, be subsets of $V$ such that $V=\\bigcup_{i=1}^{m}B_i$. Let $X_i$, $i\\in V$, be independent random variables, and let $X_{B_i}=(X_j)_{j\\in B_i}$. In this paper, we propose a recursive computation method to calculate the conditional expectation $E\\bigl[\\prod_{i=1}^m\\chi_i(X_{B_i}) \\,|\\, N\\bigr]$ with $N=\\sum_{i\\in V}X_i$ given, where $\\chi_i$ is an arbitrary function. Our method is based on the recursive summation/integration technique using the Markov property in statistics. To extract the Markov property, we define an undirected"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00108","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"}