{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IRMIUO74H4L3K35HDORMH2Z3Y3","short_pith_number":"pith:IRMIUO74","canonical_record":{"source":{"id":"1602.02279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-02-06T17:01:24Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"3adeab56c05b3cbe06d7881fa902db14b07e295d7621ffec175282ed62e7ff8f","abstract_canon_sha256":"1d55cc18721e8a9e70f057d9cb5b15ef4075ae7cdf115e076f598d76fb736183"},"schema_version":"1.0"},"canonical_sha256":"44588a3bfc3f17b56fa71ba2c3eb3bc6caf748352bbe1c126a1b1e3979064ba6","source":{"kind":"arxiv","id":"1602.02279","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02279","created_at":"2026-05-18T01:08:32Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02279v2","created_at":"2026-05-18T01:08:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02279","created_at":"2026-05-18T01:08:32Z"},{"alias_kind":"pith_short_12","alias_value":"IRMIUO74H4L3","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IRMIUO74H4L3K35H","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IRMIUO74","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IRMIUO74H4L3K35HDORMH2Z3Y3","target":"record","payload":{"canonical_record":{"source":{"id":"1602.02279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-02-06T17:01:24Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"3adeab56c05b3cbe06d7881fa902db14b07e295d7621ffec175282ed62e7ff8f","abstract_canon_sha256":"1d55cc18721e8a9e70f057d9cb5b15ef4075ae7cdf115e076f598d76fb736183"},"schema_version":"1.0"},"canonical_sha256":"44588a3bfc3f17b56fa71ba2c3eb3bc6caf748352bbe1c126a1b1e3979064ba6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:32.375764Z","signature_b64":"7rYAGsrb0PzqKUpoXrs2qBqmuGYhULxGRTEvEo/xqlC1Wi5HEVrUf8xeT4dK9eedY8yogV4CHEdR0QlXdGW7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44588a3bfc3f17b56fa71ba2c3eb3bc6caf748352bbe1c126a1b1e3979064ba6","last_reissued_at":"2026-05-18T01:08:32.375190Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:32.375190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.02279","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8MtD9Wt5iewif7QVvVfOI5Zipd4X0/E4JBPSuQGLYwGzsJ8b2zLJgb5OnDQSZJz/cgEbNOwdDVBWrHEYENN6BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:13:06.214595Z"},"content_sha256":"4cf290b18684a9e77dec4f94c4c66c89ec54ddf082bd26d876288bc96a33de70","schema_version":"1.0","event_id":"sha256:4cf290b18684a9e77dec4f94c4c66c89ec54ddf082bd26d876288bc96a33de70"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IRMIUO74H4L3K35HDORMH2Z3Y3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An algorithm for approximating the second moment of the normalizing constant estimate from a particle filter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Nick Whiteley, Svetoslav Kostov","submitted_at":"2016-02-06T17:01:24Z","abstract_excerpt":"We propose a new algorithm for approximating the non-asymptotic second moment of the marginal likelihood estimate, or normalizing constant, provided by a particle filter. The computational cost of the new method is $O(M)$ per time step, independently of the number of particles $N$ in the particle filter, where $M$ is a parameter controlling the quality of the approximation. This is in contrast to $O(MN)$ for a simple averaging technique using $M$ i.i.d. replicates of a particle filter with $N$ particles. We establish that the approximation delivered by the new algorithm is unbiased, strongly c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02279","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8/HkX2U2otNaXbADf0MCfcyvbpQKyKBwsnh36Syoytsm0GDb9+Wib37y+i39grjuU72nyUvVaYj5lmptdK6RBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:13:06.214936Z"},"content_sha256":"0692c11fc24bce27d9248c3e676ee8a5a6824ddc473bf39e505ea6447188b6a2","schema_version":"1.0","event_id":"sha256:0692c11fc24bce27d9248c3e676ee8a5a6824ddc473bf39e505ea6447188b6a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IRMIUO74H4L3K35HDORMH2Z3Y3/bundle.json","state_url":"https://pith.science/pith/IRMIUO74H4L3K35HDORMH2Z3Y3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IRMIUO74H4L3K35HDORMH2Z3Y3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-12T09:13:06Z","links":{"resolver":"https://pith.science/pith/IRMIUO74H4L3K35HDORMH2Z3Y3","bundle":"https://pith.science/pith/IRMIUO74H4L3K35HDORMH2Z3Y3/bundle.json","state":"https://pith.science/pith/IRMIUO74H4L3K35HDORMH2Z3Y3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IRMIUO74H4L3K35HDORMH2Z3Y3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IRMIUO74H4L3K35HDORMH2Z3Y3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1d55cc18721e8a9e70f057d9cb5b15ef4075ae7cdf115e076f598d76fb736183","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-02-06T17:01:24Z","title_canon_sha256":"3adeab56c05b3cbe06d7881fa902db14b07e295d7621ffec175282ed62e7ff8f"},"schema_version":"1.0","source":{"id":"1602.02279","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02279","created_at":"2026-05-18T01:08:32Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02279v2","created_at":"2026-05-18T01:08:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02279","created_at":"2026-05-18T01:08:32Z"},{"alias_kind":"pith_short_12","alias_value":"IRMIUO74H4L3","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IRMIUO74H4L3K35H","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IRMIUO74","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:0692c11fc24bce27d9248c3e676ee8a5a6824ddc473bf39e505ea6447188b6a2","target":"graph","created_at":"2026-05-18T01:08:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We propose a new algorithm for approximating the non-asymptotic second moment of the marginal likelihood estimate, or normalizing constant, provided by a particle filter. The computational cost of the new method is $O(M)$ per time step, independently of the number of particles $N$ in the particle filter, where $M$ is a parameter controlling the quality of the approximation. This is in contrast to $O(MN)$ for a simple averaging technique using $M$ i.i.d. replicates of a particle filter with $N$ particles. We establish that the approximation delivered by the new algorithm is unbiased, strongly c","authors_text":"Nick Whiteley, Svetoslav Kostov","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-02-06T17:01:24Z","title":"An algorithm for approximating the second moment of the normalizing constant estimate from a particle filter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02279","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4cf290b18684a9e77dec4f94c4c66c89ec54ddf082bd26d876288bc96a33de70","target":"record","created_at":"2026-05-18T01:08:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1d55cc18721e8a9e70f057d9cb5b15ef4075ae7cdf115e076f598d76fb736183","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2016-02-06T17:01:24Z","title_canon_sha256":"3adeab56c05b3cbe06d7881fa902db14b07e295d7621ffec175282ed62e7ff8f"},"schema_version":"1.0","source":{"id":"1602.02279","kind":"arxiv","version":2}},"canonical_sha256":"44588a3bfc3f17b56fa71ba2c3eb3bc6caf748352bbe1c126a1b1e3979064ba6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44588a3bfc3f17b56fa71ba2c3eb3bc6caf748352bbe1c126a1b1e3979064ba6","first_computed_at":"2026-05-18T01:08:32.375190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:32.375190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7rYAGsrb0PzqKUpoXrs2qBqmuGYhULxGRTEvEo/xqlC1Wi5HEVrUf8xeT4dK9eedY8yogV4CHEdR0QlXdGW7BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:32.375764Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.02279","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cf290b18684a9e77dec4f94c4c66c89ec54ddf082bd26d876288bc96a33de70","sha256:0692c11fc24bce27d9248c3e676ee8a5a6824ddc473bf39e505ea6447188b6a2"],"state_sha256":"fda288f1efed77e64eb00ca87f7bb0188a34ccbe58abb1478e1277405451144b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ft9s/1l5OeEdnUSLJQ96R/FWsM3eZZQYjHOnDcYGFkmBLqbj2QD7081OlVuN7GcGIY6o3kWgdfosth6+aeL5BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T09:13:06.217025Z","bundle_sha256":"1c0340b4ec555c370e2453cef3cec56817c7495416294000cc983cf3f94e216b"}}