{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:DAWNVVQ4SI3S3FCX5VXIVVMMO3","short_pith_number":"pith:DAWNVVQ4","canonical_record":{"source":{"id":"1903.00928","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-03-03T15:51:55Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"54a92f2bdf96c5db97ac4a2f2af313a391c64288c0f5f6eb336d1c6bd6ec9f1f","abstract_canon_sha256":"2d25b219f9d2ce8028c820610065726d4ac121dfd863f665eb7a87e0b443d16b"},"schema_version":"1.0"},"canonical_sha256":"182cdad61c92372d9457ed6e8ad58c76c427c44bc8466888c43733247d23d420","source":{"kind":"arxiv","id":"1903.00928","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00928","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00928v1","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00928","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"DAWNVVQ4SI3S","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"DAWNVVQ4SI3S3FCX","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"DAWNVVQ4","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:DAWNVVQ4SI3S3FCX5VXIVVMMO3","target":"record","payload":{"canonical_record":{"source":{"id":"1903.00928","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-03-03T15:51:55Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"54a92f2bdf96c5db97ac4a2f2af313a391c64288c0f5f6eb336d1c6bd6ec9f1f","abstract_canon_sha256":"2d25b219f9d2ce8028c820610065726d4ac121dfd863f665eb7a87e0b443d16b"},"schema_version":"1.0"},"canonical_sha256":"182cdad61c92372d9457ed6e8ad58c76c427c44bc8466888c43733247d23d420","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:12.762482Z","signature_b64":"/VYU1RJyZjF7ioL3ZaOw4mykdpSZ3GV5uWzvXJHEI4i/tM62s4jOc5QU18obQRNNvjZzN6vM/WvL+xg5Zzx2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"182cdad61c92372d9457ed6e8ad58c76c427c44bc8466888c43733247d23d420","last_reissued_at":"2026-05-17T23:52:12.761862Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:12.761862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.00928","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":"2026-05-17T23:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/8PLqAb9/vAHOSaminjc6fKAnd8kRXpLNWZL/YR8Bgew9SPumDmLEz1e9W3ozJd/JgRX5+b8eWEkGSPDOt8kDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:36:01.480545Z"},"content_sha256":"2ca7ad5d1db6ebde05b75c32b1ef1e913f0cf0f8a072e627215fa9b5fa26a1a7","schema_version":"1.0","event_id":"sha256:2ca7ad5d1db6ebde05b75c32b1ef1e913f0cf0f8a072e627215fa9b5fa26a1a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:DAWNVVQ4SI3S3FCX5VXIVVMMO3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Heavy Tailed Horseshoe Priors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Andrew Womack, Zikun Yang","submitted_at":"2019-03-03T15:51:55Z","abstract_excerpt":"Locally adaptive shrinkage in the Bayesian framework is achieved through the use of local-global prior distributions that model both the global level of sparsity as well as individual shrinkage parameters for mean structure parameters. The most popular of these models is the Horseshoe prior and its variants due to their spike and slab behavior involving an asymptote at the origin and heavy tails. In this article, we present an alternative Horseshoe prior that exhibits both a sharper asymptote at the origin as well as heavier tails, which we call the Heavy-tailed Horseshoe prior. We prove that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00928","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":"2026-05-17T23:52:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AmjVmvbFUE4ue3zpHk87JUk4hMtB8YS0Ua3Di4J6x+rtH1jlmEcnUXMdouGvnnEln4Cpwgt5vawGaeKM/X9tDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:36:01.481275Z"},"content_sha256":"6b18115146b259e273b4de1097352bae83a5914ecc4fda39f2d0411057465c8c","schema_version":"1.0","event_id":"sha256:6b18115146b259e273b4de1097352bae83a5914ecc4fda39f2d0411057465c8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DAWNVVQ4SI3S3FCX5VXIVVMMO3/bundle.json","state_url":"https://pith.science/pith/DAWNVVQ4SI3S3FCX5VXIVVMMO3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DAWNVVQ4SI3S3FCX5VXIVVMMO3/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":"2026-06-11T16:36:01Z","links":{"resolver":"https://pith.science/pith/DAWNVVQ4SI3S3FCX5VXIVVMMO3","bundle":"https://pith.science/pith/DAWNVVQ4SI3S3FCX5VXIVVMMO3/bundle.json","state":"https://pith.science/pith/DAWNVVQ4SI3S3FCX5VXIVVMMO3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DAWNVVQ4SI3S3FCX5VXIVVMMO3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DAWNVVQ4SI3S3FCX5VXIVVMMO3","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":"2d25b219f9d2ce8028c820610065726d4ac121dfd863f665eb7a87e0b443d16b","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-03-03T15:51:55Z","title_canon_sha256":"54a92f2bdf96c5db97ac4a2f2af313a391c64288c0f5f6eb336d1c6bd6ec9f1f"},"schema_version":"1.0","source":{"id":"1903.00928","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00928","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00928v1","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00928","created_at":"2026-05-17T23:52:12Z"},{"alias_kind":"pith_short_12","alias_value":"DAWNVVQ4SI3S","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"DAWNVVQ4SI3S3FCX","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"DAWNVVQ4","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:6b18115146b259e273b4de1097352bae83a5914ecc4fda39f2d0411057465c8c","target":"graph","created_at":"2026-05-17T23:52:12Z","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":"Locally adaptive shrinkage in the Bayesian framework is achieved through the use of local-global prior distributions that model both the global level of sparsity as well as individual shrinkage parameters for mean structure parameters. The most popular of these models is the Horseshoe prior and its variants due to their spike and slab behavior involving an asymptote at the origin and heavy tails. In this article, we present an alternative Horseshoe prior that exhibits both a sharper asymptote at the origin as well as heavier tails, which we call the Heavy-tailed Horseshoe prior. We prove that ","authors_text":"Andrew Womack, Zikun Yang","cross_cats":["stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-03-03T15:51:55Z","title":"Heavy Tailed Horseshoe Priors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00928","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":"sha256:2ca7ad5d1db6ebde05b75c32b1ef1e913f0cf0f8a072e627215fa9b5fa26a1a7","target":"record","created_at":"2026-05-17T23:52:12Z","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":"2d25b219f9d2ce8028c820610065726d4ac121dfd863f665eb7a87e0b443d16b","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-03-03T15:51:55Z","title_canon_sha256":"54a92f2bdf96c5db97ac4a2f2af313a391c64288c0f5f6eb336d1c6bd6ec9f1f"},"schema_version":"1.0","source":{"id":"1903.00928","kind":"arxiv","version":1}},"canonical_sha256":"182cdad61c92372d9457ed6e8ad58c76c427c44bc8466888c43733247d23d420","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"182cdad61c92372d9457ed6e8ad58c76c427c44bc8466888c43733247d23d420","first_computed_at":"2026-05-17T23:52:12.761862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:12.761862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/VYU1RJyZjF7ioL3ZaOw4mykdpSZ3GV5uWzvXJHEI4i/tM62s4jOc5QU18obQRNNvjZzN6vM/WvL+xg5Zzx2BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:12.762482Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.00928","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ca7ad5d1db6ebde05b75c32b1ef1e913f0cf0f8a072e627215fa9b5fa26a1a7","sha256:6b18115146b259e273b4de1097352bae83a5914ecc4fda39f2d0411057465c8c"],"state_sha256":"1c71a888fc8ee70c5a2dd6eba11e4551588b2a4de04f89621eb5a37d5d8f512f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FLlAXSFH5+gE57VznxQLtQZFCkOgyTuMLQPZyPaJ0gXFY3hV7EwRzmsUI92ddqOt6puuohl8DniCL+ip4BEICw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T16:36:01.485442Z","bundle_sha256":"33ffeb69f9d41266cec8c19a3583900ab6ae7988bcabcf41326cb8d7d8055e16"}}