{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JIDSLD3KAOO4FRWHOFPQWKOKND","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":"0dee36dd3ef9f4571319e7a0491c9aa36cbc28ee64c1d9a9e260ee053737b5e2","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-04T03:19:01Z","title_canon_sha256":"e015009021386be41ef13b0227b60b09a401dbe73f544e80a089affcac9893eb"},"schema_version":"1.0","source":{"id":"1102.0826","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0826","created_at":"2026-05-18T04:03:19Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0826v2","created_at":"2026-05-18T04:03:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0826","created_at":"2026-05-18T04:03:19Z"},{"alias_kind":"pith_short_12","alias_value":"JIDSLD3KAOO4","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JIDSLD3KAOO4FRWH","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JIDSLD3K","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:964ced456237e82b7ee78b276b334e6778b4ba7f7d7a9bec81141216dcacda26","target":"graph","created_at":"2026-05-18T04:03:19Z","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":"Linear models with a growing number of parameters have been widely used in modern statistics. One important problem about this kind of model is the variable selection issue. Bayesian approaches, which provide a stochastic search of informative variables, have gained popularity. In this paper, we will study the asymptotic properties related to Bayesian model selection when the model dimension $p$ is growing with the sample size $n$. We consider $p\\le n$ and provide sufficient conditions under which: (1) with large probability, the posterior probability of the true model (from which samples are ","authors_text":"Murray K. Clayton, Zuofeng Shang","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-04T03:19:01Z","title":"Consistency of Bayesian Linear Model Selection With a Growing Number of Parameters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0826","kind":"arxiv","version":2},"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:ff082f6115ed4107f0acbb5620b08d8a8399b13f5c2f4618b223ef2839014d90","target":"record","created_at":"2026-05-18T04:03:19Z","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":"0dee36dd3ef9f4571319e7a0491c9aa36cbc28ee64c1d9a9e260ee053737b5e2","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-04T03:19:01Z","title_canon_sha256":"e015009021386be41ef13b0227b60b09a401dbe73f544e80a089affcac9893eb"},"schema_version":"1.0","source":{"id":"1102.0826","kind":"arxiv","version":2}},"canonical_sha256":"4a07258f6a039dc2c6c7715f0b29ca68d4500626779fec11e7ca36940accb433","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a07258f6a039dc2c6c7715f0b29ca68d4500626779fec11e7ca36940accb433","first_computed_at":"2026-05-18T04:03:19.462575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:19.462575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lPDZ807pxHT1LUEh9yrASSaqQBX8ymeVSwU55gIqlUKEK3jvJrTQR/rfWu59jFJxTeSNZTn9Xzy2MrN6ji6/DA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:19.463054Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.0826","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff082f6115ed4107f0acbb5620b08d8a8399b13f5c2f4618b223ef2839014d90","sha256:964ced456237e82b7ee78b276b334e6778b4ba7f7d7a9bec81141216dcacda26"],"state_sha256":"b60ddcba32249df860ef4a527f0c9fc1c5cdd4169f67821b62d5f69537bf9fea"}