{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:A36VXNBLS5DLVKXDDAM63SI4MM","short_pith_number":"pith:A36VXNBL","canonical_record":{"source":{"id":"1808.05412","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-08-16T11:03:01Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"04f6e3c7b489fbe3b3ec495a26128c2fa6e42fd7885bac1e4ad368f2dd726137","abstract_canon_sha256":"135525c12f5e3149f8d7f5d7b4cb600dea466b75a2afd63cf981a67735546169"},"schema_version":"1.0"},"canonical_sha256":"06fd5bb42b9746baaae31819edc91c632a5dddc8bbd14d1bad997e3db570e359","source":{"kind":"arxiv","id":"1808.05412","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.05412","created_at":"2026-05-18T00:07:57Z"},{"alias_kind":"arxiv_version","alias_value":"1808.05412v1","created_at":"2026-05-18T00:07:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.05412","created_at":"2026-05-18T00:07:57Z"},{"alias_kind":"pith_short_12","alias_value":"A36VXNBLS5DL","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"A36VXNBLS5DLVKXD","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"A36VXNBL","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:A36VXNBLS5DLVKXDDAM63SI4MM","target":"record","payload":{"canonical_record":{"source":{"id":"1808.05412","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-08-16T11:03:01Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"04f6e3c7b489fbe3b3ec495a26128c2fa6e42fd7885bac1e4ad368f2dd726137","abstract_canon_sha256":"135525c12f5e3149f8d7f5d7b4cb600dea466b75a2afd63cf981a67735546169"},"schema_version":"1.0"},"canonical_sha256":"06fd5bb42b9746baaae31819edc91c632a5dddc8bbd14d1bad997e3db570e359","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:57.135495Z","signature_b64":"MEw+epsBn9hvw4+FiQWba+K5O5ZoVlVou1sqSseOHLqD7OrmxDrN52LOCRYOXOe/Cw2DWvGroiBApx3hCk8zAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06fd5bb42b9746baaae31819edc91c632a5dddc8bbd14d1bad997e3db570e359","last_reissued_at":"2026-05-18T00:07:57.134834Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:57.134834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.05412","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QyH3xiskLvv1uIzW/+qdXS9LpmQAGHPmdJDDnzSytbRyekc7UHtNhxYoHlkMs348ZRLLz8F8nR1jWcBzmGN8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:15:17.569139Z"},"content_sha256":"6d781d59c97ac37bd7129b67f27d0f3a7d2d884c72c2187f12cfe4d66d162af7","schema_version":"1.0","event_id":"sha256:6d781d59c97ac37bd7129b67f27d0f3a7d2d884c72c2187f12cfe4d66d162af7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:A36VXNBLS5DLVKXDDAM63SI4MM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Designs for Poisson Count Data with Gamma Block Effects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Marius Schmidt, Rainer Schwabe","submitted_at":"2018-08-16T11:03:01Z","abstract_excerpt":"The Poisson-Gamma model is a generalization of the Poisson model, which can be used for modelling count data. We show that the $D$-optimality criterion for the Poisson-Gamma model is equivalent to a combined weighted optimality criterion of $D$-optimality and $D_s$-optimality for the Poisson model. Moreover, we determine the $D$-optimal designs for the Poisson-Gamma model for multiple regression with an arbitrary number of covariates, obtaining the $D_s$-optimal designs for the Poisson and Poisson-Gamma model as a special case. For linear optimality criteria like $L$- and $c$-optimality it is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05412","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MQM/Rqa8QHjJiBHLPaVVv7twEzgOXxQZ2Fb6zoIktsKv1lsS/e9heo2QsklEPrk4z/M+FEB+Xun9cVchXLWeBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T12:15:17.569502Z"},"content_sha256":"23b0d56b21b8d399245cd232a10406c7fd60dc3e20efef77da7240c4806c50d9","schema_version":"1.0","event_id":"sha256:23b0d56b21b8d399245cd232a10406c7fd60dc3e20efef77da7240c4806c50d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A36VXNBLS5DLVKXDDAM63SI4MM/bundle.json","state_url":"https://pith.science/pith/A36VXNBLS5DLVKXDDAM63SI4MM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A36VXNBLS5DLVKXDDAM63SI4MM/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":"2026-06-26T12:15:17Z","links":{"resolver":"https://pith.science/pith/A36VXNBLS5DLVKXDDAM63SI4MM","bundle":"https://pith.science/pith/A36VXNBLS5DLVKXDDAM63SI4MM/bundle.json","state":"https://pith.science/pith/A36VXNBLS5DLVKXDDAM63SI4MM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A36VXNBLS5DLVKXDDAM63SI4MM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:A36VXNBLS5DLVKXDDAM63SI4MM","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":"135525c12f5e3149f8d7f5d7b4cb600dea466b75a2afd63cf981a67735546169","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-08-16T11:03:01Z","title_canon_sha256":"04f6e3c7b489fbe3b3ec495a26128c2fa6e42fd7885bac1e4ad368f2dd726137"},"schema_version":"1.0","source":{"id":"1808.05412","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.05412","created_at":"2026-05-18T00:07:57Z"},{"alias_kind":"arxiv_version","alias_value":"1808.05412v1","created_at":"2026-05-18T00:07:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.05412","created_at":"2026-05-18T00:07:57Z"},{"alias_kind":"pith_short_12","alias_value":"A36VXNBLS5DL","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"A36VXNBLS5DLVKXD","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"A36VXNBL","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:23b0d56b21b8d399245cd232a10406c7fd60dc3e20efef77da7240c4806c50d9","target":"graph","created_at":"2026-05-18T00:07:57Z","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":"The Poisson-Gamma model is a generalization of the Poisson model, which can be used for modelling count data. We show that the $D$-optimality criterion for the Poisson-Gamma model is equivalent to a combined weighted optimality criterion of $D$-optimality and $D_s$-optimality for the Poisson model. Moreover, we determine the $D$-optimal designs for the Poisson-Gamma model for multiple regression with an arbitrary number of covariates, obtaining the $D_s$-optimal designs for the Poisson and Poisson-Gamma model as a special case. For linear optimality criteria like $L$- and $c$-optimality it is ","authors_text":"Marius Schmidt, Rainer Schwabe","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-08-16T11:03:01Z","title":"Optimal Designs for Poisson Count Data with Gamma Block Effects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05412","kind":"arxiv","version":1},"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":"sha256:6d781d59c97ac37bd7129b67f27d0f3a7d2d884c72c2187f12cfe4d66d162af7","target":"record","created_at":"2026-05-18T00:07:57Z","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":"135525c12f5e3149f8d7f5d7b4cb600dea466b75a2afd63cf981a67735546169","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-08-16T11:03:01Z","title_canon_sha256":"04f6e3c7b489fbe3b3ec495a26128c2fa6e42fd7885bac1e4ad368f2dd726137"},"schema_version":"1.0","source":{"id":"1808.05412","kind":"arxiv","version":1}},"canonical_sha256":"06fd5bb42b9746baaae31819edc91c632a5dddc8bbd14d1bad997e3db570e359","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06fd5bb42b9746baaae31819edc91c632a5dddc8bbd14d1bad997e3db570e359","first_computed_at":"2026-05-18T00:07:57.134834Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:57.134834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MEw+epsBn9hvw4+FiQWba+K5O5ZoVlVou1sqSseOHLqD7OrmxDrN52LOCRYOXOe/Cw2DWvGroiBApx3hCk8zAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:57.135495Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.05412","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d781d59c97ac37bd7129b67f27d0f3a7d2d884c72c2187f12cfe4d66d162af7","sha256:23b0d56b21b8d399245cd232a10406c7fd60dc3e20efef77da7240c4806c50d9"],"state_sha256":"40ee2641b60d410551e6f4863767e81199f8c99a36e1f3204aef6ad5514458b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pz+jnfyScyyn56xIOFtlet1zEBuua2BE0xnQyOU3ULIiLviw7cqNUxTZ8JaxdSm7wqSw8oRSa5G9siKf/cp3Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T12:15:17.571515Z","bundle_sha256":"fc48408f2eb4f2eb0f563782be784efb55d129a6bede765b308d7344fecdd6c1"}}