{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:QQCCZXTKMMHUJXVVTCVR5IK4TB","short_pith_number":"pith:QQCCZXTK","canonical_record":{"source":{"id":"1901.05078","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-01-15T22:41:56Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"82e5ea75849b4e840915ba2b53db6232c53e3c26db7868c6c90914920beca904","abstract_canon_sha256":"d23f4491105c2230db651fa91aa28efbe210e60a01b7e80b64659dec362a5f48"},"schema_version":"1.0"},"canonical_sha256":"84042cde6a630f44deb598ab1ea15c987aa687f9501adfb98721b99fcf79e328","source":{"kind":"arxiv","id":"1901.05078","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.05078","created_at":"2026-05-17T23:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1901.05078v1","created_at":"2026-05-17T23:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.05078","created_at":"2026-05-17T23:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"QQCCZXTKMMHU","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QQCCZXTKMMHUJXVV","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QQCCZXTK","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:QQCCZXTKMMHUJXVVTCVR5IK4TB","target":"record","payload":{"canonical_record":{"source":{"id":"1901.05078","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-01-15T22:41:56Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"82e5ea75849b4e840915ba2b53db6232c53e3c26db7868c6c90914920beca904","abstract_canon_sha256":"d23f4491105c2230db651fa91aa28efbe210e60a01b7e80b64659dec362a5f48"},"schema_version":"1.0"},"canonical_sha256":"84042cde6a630f44deb598ab1ea15c987aa687f9501adfb98721b99fcf79e328","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:12.017341Z","signature_b64":"a3m1QspTbu7RZe+ENHyB6DRqRj0E+WNtRZ3pNDhk4yj/f/tm97enQTStkXItzAkT1j3N1UKvLWVscZqSjhWtDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84042cde6a630f44deb598ab1ea15c987aa687f9501adfb98721b99fcf79e328","last_reissued_at":"2026-05-17T23:56:12.016705Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:12.016705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.05078","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":"2026-05-17T23:56:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vp0dYgIK+iF6r7C0dQkgqivbs/sQTPlVGQzj1IbLHtcq5r94fYSjck6PMXY6zonBqHTZenuA+PycCkgJDH09Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:48:34.606130Z"},"content_sha256":"f26212ada3e8a20531084211e233846d2d4e72117da19d6970f95e28b66e6d12","schema_version":"1.0","event_id":"sha256:f26212ada3e8a20531084211e233846d2d4e72117da19d6970f95e28b66e6d12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:QQCCZXTKMMHUJXVVTCVR5IK4TB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On posterior contraction of parameters and interpretability in Bayesian mixture modeling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Aritra Guha, Nhat Ho, XuanLong Nguyen","submitted_at":"2019-01-15T22:41:56Z","abstract_excerpt":"We study posterior contraction behaviors for parameters of interest in the context of Bayesian mixture modeling, where the number of mixing components is unknown while the model itself may or may not be correctly specified. Two representative types of prior specification will be considered: one requires explicitly a prior distribution on the number of mixture components, while the other places a nonparametric prior on the space of mixing distributions. The former is shown to yield an optimal rate of posterior contraction on the model parameters under minimal conditions, while the latter can be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.05078","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":"2026-05-17T23:56:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zXy+4SrmlPYweDA/pAnOtzGr8tcebibD2bAAEOyUPJD4KMSOAt+8h9FoG4FRdipDQiMF37QO+tyVtCUGRELEDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:48:34.606867Z"},"content_sha256":"44e6bb4faf9b48890798e12e6a61e173c7231692ee6551acc1b7a40cdba93a09","schema_version":"1.0","event_id":"sha256:44e6bb4faf9b48890798e12e6a61e173c7231692ee6551acc1b7a40cdba93a09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QQCCZXTKMMHUJXVVTCVR5IK4TB/bundle.json","state_url":"https://pith.science/pith/QQCCZXTKMMHUJXVVTCVR5IK4TB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QQCCZXTKMMHUJXVVTCVR5IK4TB/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":"2026-05-31T19:48:34Z","links":{"resolver":"https://pith.science/pith/QQCCZXTKMMHUJXVVTCVR5IK4TB","bundle":"https://pith.science/pith/QQCCZXTKMMHUJXVVTCVR5IK4TB/bundle.json","state":"https://pith.science/pith/QQCCZXTKMMHUJXVVTCVR5IK4TB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QQCCZXTKMMHUJXVVTCVR5IK4TB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QQCCZXTKMMHUJXVVTCVR5IK4TB","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":"d23f4491105c2230db651fa91aa28efbe210e60a01b7e80b64659dec362a5f48","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-01-15T22:41:56Z","title_canon_sha256":"82e5ea75849b4e840915ba2b53db6232c53e3c26db7868c6c90914920beca904"},"schema_version":"1.0","source":{"id":"1901.05078","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.05078","created_at":"2026-05-17T23:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1901.05078v1","created_at":"2026-05-17T23:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.05078","created_at":"2026-05-17T23:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"QQCCZXTKMMHU","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QQCCZXTKMMHUJXVV","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QQCCZXTK","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:44e6bb4faf9b48890798e12e6a61e173c7231692ee6551acc1b7a40cdba93a09","target":"graph","created_at":"2026-05-17T23:56:12Z","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":"We study posterior contraction behaviors for parameters of interest in the context of Bayesian mixture modeling, where the number of mixing components is unknown while the model itself may or may not be correctly specified. Two representative types of prior specification will be considered: one requires explicitly a prior distribution on the number of mixture components, while the other places a nonparametric prior on the space of mixing distributions. The former is shown to yield an optimal rate of posterior contraction on the model parameters under minimal conditions, while the latter can be","authors_text":"Aritra Guha, Nhat Ho, XuanLong Nguyen","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-01-15T22:41:56Z","title":"On posterior contraction of parameters and interpretability in Bayesian mixture modeling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.05078","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:f26212ada3e8a20531084211e233846d2d4e72117da19d6970f95e28b66e6d12","target":"record","created_at":"2026-05-17T23:56:12Z","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":"d23f4491105c2230db651fa91aa28efbe210e60a01b7e80b64659dec362a5f48","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2019-01-15T22:41:56Z","title_canon_sha256":"82e5ea75849b4e840915ba2b53db6232c53e3c26db7868c6c90914920beca904"},"schema_version":"1.0","source":{"id":"1901.05078","kind":"arxiv","version":1}},"canonical_sha256":"84042cde6a630f44deb598ab1ea15c987aa687f9501adfb98721b99fcf79e328","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84042cde6a630f44deb598ab1ea15c987aa687f9501adfb98721b99fcf79e328","first_computed_at":"2026-05-17T23:56:12.016705Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:12.016705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a3m1QspTbu7RZe+ENHyB6DRqRj0E+WNtRZ3pNDhk4yj/f/tm97enQTStkXItzAkT1j3N1UKvLWVscZqSjhWtDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:12.017341Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.05078","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f26212ada3e8a20531084211e233846d2d4e72117da19d6970f95e28b66e6d12","sha256:44e6bb4faf9b48890798e12e6a61e173c7231692ee6551acc1b7a40cdba93a09"],"state_sha256":"e50f3b829d3e7de5f8d1b6cbc516863ad45641c98bc27d3c03cc8d7d5251896c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nlbpY3pQtrqWR++InMAjjtuk21S0ICbcwK/HI2MhPbs9m7t+ddg/JjmuTO7ZIR4XMtftPn8IEz14s2FnvQALBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T19:48:34.610822Z","bundle_sha256":"252ca507278f1aa87f3db89d9a5a4effc8ba0a53371524172bde3600e99df40a"}}