{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:A36VXNBLS5DLVKXDDAM63SI4MM","short_pith_number":"pith:A36VXNBL","schema_version":"1.0","canonical_sha256":"06fd5bb42b9746baaae31819edc91c632a5dddc8bbd14d1bad997e3db570e359","source":{"kind":"arxiv","id":"1808.05412","version":1},"attestation_state":"computed","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 "},"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":"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"},"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"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1808.05412","created_at":"2026-05-18T00:07:57.134936+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.05412v1","created_at":"2026-05-18T00:07:57.134936+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.05412","created_at":"2026-05-18T00:07:57.134936+00:00"},{"alias_kind":"pith_short_12","alias_value":"A36VXNBLS5DL","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"A36VXNBLS5DLVKXD","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"A36VXNBL","created_at":"2026-05-18T12:32:13.499390+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/A36VXNBLS5DLVKXDDAM63SI4MM","json":"https://pith.science/pith/A36VXNBLS5DLVKXDDAM63SI4MM.json","graph_json":"https://pith.science/api/pith-number/A36VXNBLS5DLVKXDDAM63SI4MM/graph.json","events_json":"https://pith.science/api/pith-number/A36VXNBLS5DLVKXDDAM63SI4MM/events.json","paper":"https://pith.science/paper/A36VXNBL"},"agent_actions":{"view_html":"https://pith.science/pith/A36VXNBLS5DLVKXDDAM63SI4MM","download_json":"https://pith.science/pith/A36VXNBLS5DLVKXDDAM63SI4MM.json","view_paper":"https://pith.science/paper/A36VXNBL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.05412&json=true","fetch_graph":"https://pith.science/api/pith-number/A36VXNBLS5DLVKXDDAM63SI4MM/graph.json","fetch_events":"https://pith.science/api/pith-number/A36VXNBLS5DLVKXDDAM63SI4MM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A36VXNBLS5DLVKXDDAM63SI4MM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A36VXNBLS5DLVKXDDAM63SI4MM/action/storage_attestation","attest_author":"https://pith.science/pith/A36VXNBLS5DLVKXDDAM63SI4MM/action/author_attestation","sign_citation":"https://pith.science/pith/A36VXNBLS5DLVKXDDAM63SI4MM/action/citation_signature","submit_replication":"https://pith.science/pith/A36VXNBLS5DLVKXDDAM63SI4MM/action/replication_record"}},"created_at":"2026-05-18T00:07:57.134936+00:00","updated_at":"2026-05-18T00:07:57.134936+00:00"}