{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Q7IRWK7WJD36M4SWN3DXRUJEVX","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":"712c54f643d3534ffc81bb2eb5b4833693756a08ca9d6b7ea92580dc9cab5f7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-10-21T00:21:30Z","title_canon_sha256":"f167a29ee0acc92f593dfcfffebfcb5e2e0e5e47b26dc55e52886b23bb6b1709"},"schema_version":"1.0","source":{"id":"1610.06632","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06632","created_at":"2026-05-18T01:01:37Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06632v1","created_at":"2026-05-18T01:01:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06632","created_at":"2026-05-18T01:01:37Z"},{"alias_kind":"pith_short_12","alias_value":"Q7IRWK7WJD36","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q7IRWK7WJD36M4SW","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q7IRWK7W","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:c4404ea166f64b9b31c2697297264ffc24341089c081b619dd742ef732f49a0e","target":"graph","created_at":"2026-05-18T01:01:37Z","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":"We consider posterior sampling in the very common Bayesian hierarchical model in which observed data depends on high-dimensional latent variables that, in turn, depend on relatively few hyperparameters. When the full conditional over the latent variables has a known form, the marginal posterior distribution over hyperparameters is accessible and can be sampled using a Markov chain Monte Carlo (MCMC) method on a low-dimensional parameter space. This may improve computational efficiency over standard Gibbs sampling since computation is not over the high-dimensional space of latent variables and ","authors_text":"Colin Fox, J. Andres Christen, Richard A. Norton","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-10-21T00:21:30Z","title":"Sampling hyperparameters in hierarchical models: improving on Gibbs for high-dimensional latent fields and large data sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06632","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:a0afb8b1f351cf9af01db8a966bf52493337d86ac9a7bd3c2281e6247cfbe3f6","target":"record","created_at":"2026-05-18T01:01:37Z","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":"712c54f643d3534ffc81bb2eb5b4833693756a08ca9d6b7ea92580dc9cab5f7a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2016-10-21T00:21:30Z","title_canon_sha256":"f167a29ee0acc92f593dfcfffebfcb5e2e0e5e47b26dc55e52886b23bb6b1709"},"schema_version":"1.0","source":{"id":"1610.06632","kind":"arxiv","version":1}},"canonical_sha256":"87d11b2bf648f7e672566ec778d124add6db9c80fff60ed0af2b04e08c1e6c7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87d11b2bf648f7e672566ec778d124add6db9c80fff60ed0af2b04e08c1e6c7b","first_computed_at":"2026-05-18T01:01:37.185591Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:37.185591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jDrsxRgfNZNRk6xo0AQ7uKi7UArsXPi1XyGxv6Wq/CALxfqBKfjmZmhUnonpGuBn9CnD/i5gjObUj6DUIjETDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:37.186310Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06632","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0afb8b1f351cf9af01db8a966bf52493337d86ac9a7bd3c2281e6247cfbe3f6","sha256:c4404ea166f64b9b31c2697297264ffc24341089c081b619dd742ef732f49a0e"],"state_sha256":"0139a70f63fccfa0ef32562d402b9fce551e32fb4dc9556e5b20a1df7ab171d8"}