{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:AYCJVZU7YPF44CQUW2K44C6LT7","short_pith_number":"pith:AYCJVZU7","canonical_record":{"source":{"id":"1002.3786","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-02-19T17:08:54Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"32d32b6969ea2b72d38e623208ea3a0b15f85281a419e08d802d3191c0977ffc","abstract_canon_sha256":"fbda6b800244753ef19f24c43f6d3273867acb839e086cce2b71ef80a514d83d"},"schema_version":"1.0"},"canonical_sha256":"06049ae69fc3cbce0a14b695ce0bcb9fe4573d3b495de4b740877e5509ddef1f","source":{"kind":"arxiv","id":"1002.3786","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3786","created_at":"2026-05-18T03:31:31Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3786v1","created_at":"2026-05-18T03:31:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3786","created_at":"2026-05-18T03:31:31Z"},{"alias_kind":"pith_short_12","alias_value":"AYCJVZU7YPF4","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AYCJVZU7YPF44CQU","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AYCJVZU7","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:AYCJVZU7YPF44CQUW2K44C6LT7","target":"record","payload":{"canonical_record":{"source":{"id":"1002.3786","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-02-19T17:08:54Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"32d32b6969ea2b72d38e623208ea3a0b15f85281a419e08d802d3191c0977ffc","abstract_canon_sha256":"fbda6b800244753ef19f24c43f6d3273867acb839e086cce2b71ef80a514d83d"},"schema_version":"1.0"},"canonical_sha256":"06049ae69fc3cbce0a14b695ce0bcb9fe4573d3b495de4b740877e5509ddef1f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:31.203921Z","signature_b64":"1R37E4vCXaTLAelFtbQBxMOv0mOiZ6MUjkIOXxTBPXmR7E53uHyuuQa3DB0vilSgDW9AIZ7ZdhXGCW9X7D8dAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06049ae69fc3cbce0a14b695ce0bcb9fe4573d3b495de4b740877e5509ddef1f","last_reissued_at":"2026-05-18T03:31:31.203017Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:31.203017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.3786","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":"2026-05-18T03:31:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MUN5Vi/MmTQltrKzQDPuE3RPEWAdKQYmIqr4uFv+DnPZCZXhXABaatAODdltIbXsO9LPRvF4EdYgJkGayQJoDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:02:14.824017Z"},"content_sha256":"fae51390c9f72d1d48ed6e2e571769693f81ce36e679d83bccacb123e94db7b9","schema_version":"1.0","event_id":"sha256:fae51390c9f72d1d48ed6e2e571769693f81ce36e679d83bccacb123e94db7b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:AYCJVZU7YPF44CQUW2K44C6LT7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bayesian predictive densities for linear regression models under alpha-divergence loss: some results and open problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"William E. Strawderman, Yuzo Maruyama","submitted_at":"2010-02-19T17:08:54Z","abstract_excerpt":"This paper considers estimation of the predictive density for a normal linear model with unknown variance under alpha-divergence loss for -1 <= alpha <= 1. We first give a general canonical form for the problem, and then give general expressions for the generalized Bayes solution under the above loss for each alpha. For a particular class of hierarchical generalized priors studied in Maruyama and Strawderman (2005, 2006) for the problems of estimating the mean vector and the variance respectively, we give the generalized Bayes predictive density. Additionally, we show that, for a subclass of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3786","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":"2026-05-18T03:31:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2rRuaATIe2LYmmv4lYpPVbu/jYuttC1QAEP1h/I//36VMqB/uiiLVqe4w5Sa9Y2LLbp0SVleR4JpRroGqt7zBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:02:14.824373Z"},"content_sha256":"e226ad0c10f338a39d432dc2c50b26eb770c1365f4a1e002c76a6edd230c1b50","schema_version":"1.0","event_id":"sha256:e226ad0c10f338a39d432dc2c50b26eb770c1365f4a1e002c76a6edd230c1b50"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AYCJVZU7YPF44CQUW2K44C6LT7/bundle.json","state_url":"https://pith.science/pith/AYCJVZU7YPF44CQUW2K44C6LT7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AYCJVZU7YPF44CQUW2K44C6LT7/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":"2026-06-24T11:02:14Z","links":{"resolver":"https://pith.science/pith/AYCJVZU7YPF44CQUW2K44C6LT7","bundle":"https://pith.science/pith/AYCJVZU7YPF44CQUW2K44C6LT7/bundle.json","state":"https://pith.science/pith/AYCJVZU7YPF44CQUW2K44C6LT7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AYCJVZU7YPF44CQUW2K44C6LT7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:AYCJVZU7YPF44CQUW2K44C6LT7","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":"fbda6b800244753ef19f24c43f6d3273867acb839e086cce2b71ef80a514d83d","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-02-19T17:08:54Z","title_canon_sha256":"32d32b6969ea2b72d38e623208ea3a0b15f85281a419e08d802d3191c0977ffc"},"schema_version":"1.0","source":{"id":"1002.3786","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3786","created_at":"2026-05-18T03:31:31Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3786v1","created_at":"2026-05-18T03:31:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3786","created_at":"2026-05-18T03:31:31Z"},{"alias_kind":"pith_short_12","alias_value":"AYCJVZU7YPF4","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AYCJVZU7YPF44CQU","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AYCJVZU7","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:e226ad0c10f338a39d432dc2c50b26eb770c1365f4a1e002c76a6edd230c1b50","target":"graph","created_at":"2026-05-18T03:31:31Z","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":"This paper considers estimation of the predictive density for a normal linear model with unknown variance under alpha-divergence loss for -1 <= alpha <= 1. We first give a general canonical form for the problem, and then give general expressions for the generalized Bayes solution under the above loss for each alpha. For a particular class of hierarchical generalized priors studied in Maruyama and Strawderman (2005, 2006) for the problems of estimating the mean vector and the variance respectively, we give the generalized Bayes predictive density. Additionally, we show that, for a subclass of t","authors_text":"William E. Strawderman, Yuzo Maruyama","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-02-19T17:08:54Z","title":"Bayesian predictive densities for linear regression models under alpha-divergence loss: some results and open problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3786","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:fae51390c9f72d1d48ed6e2e571769693f81ce36e679d83bccacb123e94db7b9","target":"record","created_at":"2026-05-18T03:31:31Z","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":"fbda6b800244753ef19f24c43f6d3273867acb839e086cce2b71ef80a514d83d","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-02-19T17:08:54Z","title_canon_sha256":"32d32b6969ea2b72d38e623208ea3a0b15f85281a419e08d802d3191c0977ffc"},"schema_version":"1.0","source":{"id":"1002.3786","kind":"arxiv","version":1}},"canonical_sha256":"06049ae69fc3cbce0a14b695ce0bcb9fe4573d3b495de4b740877e5509ddef1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06049ae69fc3cbce0a14b695ce0bcb9fe4573d3b495de4b740877e5509ddef1f","first_computed_at":"2026-05-18T03:31:31.203017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:31.203017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1R37E4vCXaTLAelFtbQBxMOv0mOiZ6MUjkIOXxTBPXmR7E53uHyuuQa3DB0vilSgDW9AIZ7ZdhXGCW9X7D8dAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:31.203921Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.3786","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fae51390c9f72d1d48ed6e2e571769693f81ce36e679d83bccacb123e94db7b9","sha256:e226ad0c10f338a39d432dc2c50b26eb770c1365f4a1e002c76a6edd230c1b50"],"state_sha256":"915e7a2fdd709770c24d80d31d2246f1dc54228719a7387fec3d3dd29f023894"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YGL0SgVNJ81nv4+LZX4SymCtgatF1H4oXdzj8FGahBWc3RvCt9PBkZxG5uh7jxn1WZ7pZ2PcIFIT1cuKK3TAAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T11:02:14.826264Z","bundle_sha256":"f834a44a4effa0b425d61ec35648a7d948ab5d87410cc4ae6d83961d6a7412e3"}}