{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CQJD3MJPQOTYGZH54NNLK4RGSM","short_pith_number":"pith:CQJD3MJP","canonical_record":{"source":{"id":"1112.1788","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-12-08T09:18:04Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"4a8064ea64c24172c61fc98e2b572d86d7d506da32c93826186d759bda0502e2","abstract_canon_sha256":"8ed3525675f66e1616f6b656ef1417457644b21fc162901f35d35529d28d8c54"},"schema_version":"1.0"},"canonical_sha256":"14123db12f83a78364fde35ab57226933826f7e47d4eabaec8b517c87e53754e","source":{"kind":"arxiv","id":"1112.1788","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1788","created_at":"2026-05-18T04:00:15Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1788v3","created_at":"2026-05-18T04:00:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1788","created_at":"2026-05-18T04:00:15Z"},{"alias_kind":"pith_short_12","alias_value":"CQJD3MJPQOTY","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CQJD3MJPQOTYGZH5","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CQJD3MJP","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CQJD3MJPQOTYGZH54NNLK4RGSM","target":"record","payload":{"canonical_record":{"source":{"id":"1112.1788","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-12-08T09:18:04Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"4a8064ea64c24172c61fc98e2b572d86d7d506da32c93826186d759bda0502e2","abstract_canon_sha256":"8ed3525675f66e1616f6b656ef1417457644b21fc162901f35d35529d28d8c54"},"schema_version":"1.0"},"canonical_sha256":"14123db12f83a78364fde35ab57226933826f7e47d4eabaec8b517c87e53754e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:15.377807Z","signature_b64":"aJBZDjg4Yf7EUQvFq315t1R3znZMpDrpTYL6tvCGpQIDq+xvDk4uUJgiKuC8yYrpxvqMIK78Crda6lKY4RdzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14123db12f83a78364fde35ab57226933826f7e47d4eabaec8b517c87e53754e","last_reissued_at":"2026-05-18T04:00:15.377040Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:15.377040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.1788","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:00:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CWXvPj/uTQ/yzZLLVmokCkPJOgUgm2qPxZ5FjQCKJyRkbWo5YPbrZLkQNuYLIR1lGIiV2vJe/VLueUf3QGNPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:18:24.980736Z"},"content_sha256":"0040e81e4cbba8c36deafca105d13ae5121d769599d2c396f3d9b763dcfebe92","schema_version":"1.0","event_id":"sha256:0040e81e4cbba8c36deafca105d13ae5121d769599d2c396f3d9b763dcfebe92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CQJD3MJPQOTYGZH54NNLK4RGSM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Hoeffding-Sobol Decomposition for Dependent Variables -Application to Sensitivity Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Cl\\'ementine Prieur (M\\'ethodes d'Analyse Stochastique des Codes et Traitements Num\\'eriques, Fabrice Gamboa (M\\'ethodes d'Analyse Stochastique des Codes et Traitements Num\\'eriques, Ga\\\"elle Chastaing (M\\'ethodes d'Analyse Stochastique des Codes et Traitements Num\\'eriques, IMT), INRIA Grenoble Rh\\^one-Alpes / LJK Laboratoire Jean Kuntzmann)","submitted_at":"2011-12-08T09:18:04Z","abstract_excerpt":"In this paper, we consider a regression model built on dependent variables. This regression modelizes an input output relationship. Under boundedness assumptions on the joint distribution function of the input variables, we show that a generalized Hoeffding-Sobol decomposition is available. This leads to new indices measuring the sensitivity of the output with respect to the input variables. We also study and discuss the estimation of these new indices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1788","kind":"arxiv","version":3},"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":"2026-05-18T04:00:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ybqaBrFYbp/tLj/m20dljv3b9B8ikR+8LgIfxCR3CAWb5236jig5uuvPWnQUxujctUYbw24Wv7qoCsp5HpSeAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:18:24.981191Z"},"content_sha256":"127e34b05e1d9ea8b280b6350e7952c165c71e11561598d32a309c1e9994f737","schema_version":"1.0","event_id":"sha256:127e34b05e1d9ea8b280b6350e7952c165c71e11561598d32a309c1e9994f737"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CQJD3MJPQOTYGZH54NNLK4RGSM/bundle.json","state_url":"https://pith.science/pith/CQJD3MJPQOTYGZH54NNLK4RGSM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CQJD3MJPQOTYGZH54NNLK4RGSM/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":"2026-05-31T22:18:24Z","links":{"resolver":"https://pith.science/pith/CQJD3MJPQOTYGZH54NNLK4RGSM","bundle":"https://pith.science/pith/CQJD3MJPQOTYGZH54NNLK4RGSM/bundle.json","state":"https://pith.science/pith/CQJD3MJPQOTYGZH54NNLK4RGSM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CQJD3MJPQOTYGZH54NNLK4RGSM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CQJD3MJPQOTYGZH54NNLK4RGSM","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":"8ed3525675f66e1616f6b656ef1417457644b21fc162901f35d35529d28d8c54","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-12-08T09:18:04Z","title_canon_sha256":"4a8064ea64c24172c61fc98e2b572d86d7d506da32c93826186d759bda0502e2"},"schema_version":"1.0","source":{"id":"1112.1788","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1788","created_at":"2026-05-18T04:00:15Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1788v3","created_at":"2026-05-18T04:00:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1788","created_at":"2026-05-18T04:00:15Z"},{"alias_kind":"pith_short_12","alias_value":"CQJD3MJPQOTY","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CQJD3MJPQOTYGZH5","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CQJD3MJP","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:127e34b05e1d9ea8b280b6350e7952c165c71e11561598d32a309c1e9994f737","target":"graph","created_at":"2026-05-18T04:00:15Z","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":"In this paper, we consider a regression model built on dependent variables. This regression modelizes an input output relationship. Under boundedness assumptions on the joint distribution function of the input variables, we show that a generalized Hoeffding-Sobol decomposition is available. This leads to new indices measuring the sensitivity of the output with respect to the input variables. We also study and discuss the estimation of these new indices.","authors_text":"Cl\\'ementine Prieur (M\\'ethodes d'Analyse Stochastique des Codes et Traitements Num\\'eriques, Fabrice Gamboa (M\\'ethodes d'Analyse Stochastique des Codes et Traitements Num\\'eriques, Ga\\\"elle Chastaing (M\\'ethodes d'Analyse Stochastique des Codes et Traitements Num\\'eriques, IMT), INRIA Grenoble Rh\\^one-Alpes / LJK Laboratoire Jean Kuntzmann)","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-12-08T09:18:04Z","title":"Generalized Hoeffding-Sobol Decomposition for Dependent Variables -Application to Sensitivity Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1788","kind":"arxiv","version":3},"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":"sha256:0040e81e4cbba8c36deafca105d13ae5121d769599d2c396f3d9b763dcfebe92","target":"record","created_at":"2026-05-18T04:00:15Z","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":"8ed3525675f66e1616f6b656ef1417457644b21fc162901f35d35529d28d8c54","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-12-08T09:18:04Z","title_canon_sha256":"4a8064ea64c24172c61fc98e2b572d86d7d506da32c93826186d759bda0502e2"},"schema_version":"1.0","source":{"id":"1112.1788","kind":"arxiv","version":3}},"canonical_sha256":"14123db12f83a78364fde35ab57226933826f7e47d4eabaec8b517c87e53754e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14123db12f83a78364fde35ab57226933826f7e47d4eabaec8b517c87e53754e","first_computed_at":"2026-05-18T04:00:15.377040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:15.377040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aJBZDjg4Yf7EUQvFq315t1R3znZMpDrpTYL6tvCGpQIDq+xvDk4uUJgiKuC8yYrpxvqMIK78Crda6lKY4RdzCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:15.377807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1788","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0040e81e4cbba8c36deafca105d13ae5121d769599d2c396f3d9b763dcfebe92","sha256:127e34b05e1d9ea8b280b6350e7952c165c71e11561598d32a309c1e9994f737"],"state_sha256":"cc422768c5994cab818ffc08b42ceb76fdd6b83c7a0acbf0c7aec10bb4830941"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IpnqC1lDnAkEnPnP2/G5SIuT2CfmQ0/1SMC2CHzAnqVnTKrER1677Q82YpTEes+opCb5a7a1WFYIcwJqNN/wDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T22:18:24.985015Z","bundle_sha256":"7b2815be86528d1a1354dc3e9184bae3fe4928dfacbb8cac78774453c3211763"}}