{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:LYBEIHETWU6W2SA4W2D2DFZNOQ","short_pith_number":"pith:LYBEIHET","schema_version":"1.0","canonical_sha256":"5e02441c93b53d6d481cb687a1972d74117973a854d08739843cdfce25a9c8ba","source":{"kind":"arxiv","id":"1211.4483","version":1},"attestation_state":"computed","paper":{"title":"Computational aspects of Bayesian spectral density estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME"],"primary_cat":"stat.CO","authors_text":"Brunero Liseo, Judith Rousseau, Nicolas Chopin","submitted_at":"2012-11-19T16:24:40Z","abstract_excerpt":"Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of the likelihood for such models. We propose to sample from the approximate posterior (that is, the prior times the approximate likelihood), and then to recover the exact posterior through importance sampling. We show that the variance of the importance sampling weights vanishes as the sample size goes to infinity. We explain why the approximate posterior may"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1211.4483","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2012-11-19T16:24:40Z","cross_cats_sorted":["stat.ME"],"title_canon_sha256":"259abf43b27d1682ffafd302f8101e12d9d59ba0314c077b1b169ca6263dc504","abstract_canon_sha256":"a8e95517fc03b2a547e062873cee47c2ce886a328f413e5ecdba10edd7a886dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:26.746521Z","signature_b64":"PZ1wTcMTApb6Uf3K2Y8UBculQO0rV+hS/VJck1VaHLEpfQB4YFsTj43WTMz+UyGtreejW9iKdksWRWTZm59LCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e02441c93b53d6d481cb687a1972d74117973a854d08739843cdfce25a9c8ba","last_reissued_at":"2026-05-18T03:40:26.745987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:26.745987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computational aspects of Bayesian spectral density estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME"],"primary_cat":"stat.CO","authors_text":"Brunero Liseo, Judith Rousseau, Nicolas Chopin","submitted_at":"2012-11-19T16:24:40Z","abstract_excerpt":"Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of the likelihood for such models. We propose to sample from the approximate posterior (that is, the prior times the approximate likelihood), and then to recover the exact posterior through importance sampling. We show that the variance of the importance sampling weights vanishes as the sample size goes to infinity. We explain why the approximate posterior may"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4483","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1211.4483","created_at":"2026-05-18T03:40:26.746078+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.4483v1","created_at":"2026-05-18T03:40:26.746078+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4483","created_at":"2026-05-18T03:40:26.746078+00:00"},{"alias_kind":"pith_short_12","alias_value":"LYBEIHETWU6W","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"LYBEIHETWU6W2SA4","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"LYBEIHET","created_at":"2026-05-18T12:27:14.488303+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LYBEIHETWU6W2SA4W2D2DFZNOQ","json":"https://pith.science/pith/LYBEIHETWU6W2SA4W2D2DFZNOQ.json","graph_json":"https://pith.science/api/pith-number/LYBEIHETWU6W2SA4W2D2DFZNOQ/graph.json","events_json":"https://pith.science/api/pith-number/LYBEIHETWU6W2SA4W2D2DFZNOQ/events.json","paper":"https://pith.science/paper/LYBEIHET"},"agent_actions":{"view_html":"https://pith.science/pith/LYBEIHETWU6W2SA4W2D2DFZNOQ","download_json":"https://pith.science/pith/LYBEIHETWU6W2SA4W2D2DFZNOQ.json","view_paper":"https://pith.science/paper/LYBEIHET","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.4483&json=true","fetch_graph":"https://pith.science/api/pith-number/LYBEIHETWU6W2SA4W2D2DFZNOQ/graph.json","fetch_events":"https://pith.science/api/pith-number/LYBEIHETWU6W2SA4W2D2DFZNOQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LYBEIHETWU6W2SA4W2D2DFZNOQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LYBEIHETWU6W2SA4W2D2DFZNOQ/action/storage_attestation","attest_author":"https://pith.science/pith/LYBEIHETWU6W2SA4W2D2DFZNOQ/action/author_attestation","sign_citation":"https://pith.science/pith/LYBEIHETWU6W2SA4W2D2DFZNOQ/action/citation_signature","submit_replication":"https://pith.science/pith/LYBEIHETWU6W2SA4W2D2DFZNOQ/action/replication_record"}},"created_at":"2026-05-18T03:40:26.746078+00:00","updated_at":"2026-05-18T03:40:26.746078+00:00"}