{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:JY2UCP4M3WLQH2HIBXVTTPQAYX","short_pith_number":"pith:JY2UCP4M","schema_version":"1.0","canonical_sha256":"4e35413f8cdd9703e8e80deb39be00c5cbfa132cf9ef896ee187de7475a9f51d","source":{"kind":"arxiv","id":"2106.03322","version":4},"attestation_state":"computed","paper":{"title":"Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME"],"primary_cat":"stat.AP","authors_text":"Athena Dai, Edwin Ng, Zhishi Wang","submitted_at":"2021-06-07T03:38:29Z","abstract_excerpt":"Both Bayesian and varying coefficient models are very useful tools in practice as they can be used to model parameter heterogeneity in a generalizable way. Motivated by the need of enhancing Marketing Mix Modeling at Uber, we propose a Bayesian Time Varying Coefficient model, equipped with a hierarchical Bayesian structure. This model is different from other time varying coefficient models in the sense that the coefficients are weighted over a set of local latent variables following certain probabilistic distributions. Stochastic Variational Inference is used to approximate the posteriors of l"},"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":"2106.03322","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.AP","submitted_at":"2021-06-07T03:38:29Z","cross_cats_sorted":["stat.ME"],"title_canon_sha256":"eb538155a1dfa040329ebf9ebce742eb54b62c85a91dd5233891057da589f6f6","abstract_canon_sha256":"57d01817592f98aaeb33f9c36bb7e000d94e7867c6161d8ab0a59a90d3cc24bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:54:41.659013Z","signature_b64":"d7r+2/oYjcb4S3YosQ1mq863bNF+JYL8fogJrwQBzlMf7UkS80zhqYq9bKRsarSjDQhB1BU1drXzBKZsENmHAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e35413f8cdd9703e8e80deb39be00c5cbfa132cf9ef896ee187de7475a9f51d","last_reissued_at":"2026-07-05T09:54:41.658456Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:54:41.658456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bayesian Time Varying Coefficient Model with Applications to Marketing Mix Modeling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME"],"primary_cat":"stat.AP","authors_text":"Athena Dai, Edwin Ng, Zhishi Wang","submitted_at":"2021-06-07T03:38:29Z","abstract_excerpt":"Both Bayesian and varying coefficient models are very useful tools in practice as they can be used to model parameter heterogeneity in a generalizable way. Motivated by the need of enhancing Marketing Mix Modeling at Uber, we propose a Bayesian Time Varying Coefficient model, equipped with a hierarchical Bayesian structure. This model is different from other time varying coefficient models in the sense that the coefficients are weighted over a set of local latent variables following certain probabilistic distributions. Stochastic Variational Inference is used to approximate the posteriors of l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.03322","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.03322/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2106.03322","created_at":"2026-07-05T09:54:41.658527+00:00"},{"alias_kind":"arxiv_version","alias_value":"2106.03322v4","created_at":"2026-07-05T09:54:41.658527+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.03322","created_at":"2026-07-05T09:54:41.658527+00:00"},{"alias_kind":"pith_short_12","alias_value":"JY2UCP4M3WLQ","created_at":"2026-07-05T09:54:41.658527+00:00"},{"alias_kind":"pith_short_16","alias_value":"JY2UCP4M3WLQH2HI","created_at":"2026-07-05T09:54:41.658527+00:00"},{"alias_kind":"pith_short_8","alias_value":"JY2UCP4M","created_at":"2026-07-05T09:54:41.658527+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.30992","citing_title":"Hierarchical Clustering As a Novel Solution to the Notorious Multicollinearity Problem in Observational Causal Inference","ref_index":13,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JY2UCP4M3WLQH2HIBXVTTPQAYX","json":"https://pith.science/pith/JY2UCP4M3WLQH2HIBXVTTPQAYX.json","graph_json":"https://pith.science/api/pith-number/JY2UCP4M3WLQH2HIBXVTTPQAYX/graph.json","events_json":"https://pith.science/api/pith-number/JY2UCP4M3WLQH2HIBXVTTPQAYX/events.json","paper":"https://pith.science/paper/JY2UCP4M"},"agent_actions":{"view_html":"https://pith.science/pith/JY2UCP4M3WLQH2HIBXVTTPQAYX","download_json":"https://pith.science/pith/JY2UCP4M3WLQH2HIBXVTTPQAYX.json","view_paper":"https://pith.science/paper/JY2UCP4M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2106.03322&json=true","fetch_graph":"https://pith.science/api/pith-number/JY2UCP4M3WLQH2HIBXVTTPQAYX/graph.json","fetch_events":"https://pith.science/api/pith-number/JY2UCP4M3WLQH2HIBXVTTPQAYX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JY2UCP4M3WLQH2HIBXVTTPQAYX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JY2UCP4M3WLQH2HIBXVTTPQAYX/action/storage_attestation","attest_author":"https://pith.science/pith/JY2UCP4M3WLQH2HIBXVTTPQAYX/action/author_attestation","sign_citation":"https://pith.science/pith/JY2UCP4M3WLQH2HIBXVTTPQAYX/action/citation_signature","submit_replication":"https://pith.science/pith/JY2UCP4M3WLQH2HIBXVTTPQAYX/action/replication_record"}},"created_at":"2026-07-05T09:54:41.658527+00:00","updated_at":"2026-07-05T09:54:41.658527+00:00"}