{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZGI7ZASCR7JMPAA7AEGT2PFIPQ","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":"006297bbea5150038d13566cbf49508f382211cca7b9d1cc530f8f07de4525ee","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-09T12:01:36Z","title_canon_sha256":"72bd69aa5421fa1cc037e297f2f733b384b0becbbd98cf7fd14521e8f88f352c"},"schema_version":"1.0","source":{"id":"1612.02989","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02989","created_at":"2026-05-18T00:55:27Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02989v1","created_at":"2026-05-18T00:55:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02989","created_at":"2026-05-18T00:55:27Z"},{"alias_kind":"pith_short_12","alias_value":"ZGI7ZASCR7JM","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZGI7ZASCR7JMPAA7","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZGI7ZASC","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:d5294275ba738957ba5f86e96c1dc800e9092c4fd0d692bbc4e5ac28dd30fb33","target":"graph","created_at":"2026-05-18T00:55:27Z","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 introduce non-stationary Mat\\'ern field priors with stochastic partial differential equations, and construct correlation length-scaling with hyperpriors. We model both the hyperprior and the Mat\\'ern prior as continuous-parameter random fields. As hypermodels, we use Cauchy and Gaussian random fields, which we map suitably to a desired correlation length-scaling range. For computations, we discretise the models with finite difference methods. We consider the convergence of the discretised prior and posterior to the discretisation limit. We apply the developed methodology to certain interpol","authors_text":"Lassi Roininen, Mark Girolami, Markku Markkanen, Sari Lasanen","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-09T12:01:36Z","title":"Hyperpriors for Mat\\'ern fields with applications in Bayesian inversion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02989","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":"sha256:06cdaf3ceba0fe276832b50a79d3d8bfec9b1be085ca6879c7dfe372a5cad110","target":"record","created_at":"2026-05-18T00:55:27Z","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":"006297bbea5150038d13566cbf49508f382211cca7b9d1cc530f8f07de4525ee","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-12-09T12:01:36Z","title_canon_sha256":"72bd69aa5421fa1cc037e297f2f733b384b0becbbd98cf7fd14521e8f88f352c"},"schema_version":"1.0","source":{"id":"1612.02989","kind":"arxiv","version":1}},"canonical_sha256":"c991fc82428fd2c7801f010d3d3ca87c185f2cc0ac0395efc9f964a89a403eba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c991fc82428fd2c7801f010d3d3ca87c185f2cc0ac0395efc9f964a89a403eba","first_computed_at":"2026-05-18T00:55:27.763730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:27.763730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L7/K8JQJoUMpxH6WY95gGyG5b/qJWRNyWCC09H2YTgvOX+6h63ETNHm48Jf2IZjoQUTUV136CLPWUrmKzafyAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:27.764212Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.02989","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06cdaf3ceba0fe276832b50a79d3d8bfec9b1be085ca6879c7dfe372a5cad110","sha256:d5294275ba738957ba5f86e96c1dc800e9092c4fd0d692bbc4e5ac28dd30fb33"],"state_sha256":"53fdeed0b331d40cf994e3bb6b81ab736d0907c8052a5ca9797475240f60c092"}