{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:G6XIRCY3N6LT4GIF3FM2IJ5XSS","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":"57994341ceb1d64349418f79b6d4d69a01bce4cc9d6f547b572f6055a49ec885","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-02-17T14:37:43Z","title_canon_sha256":"a5608c4a573467438c1d9ae91958134e84001216c5e649d26c6c57eeec706120"},"schema_version":"1.0","source":{"id":"1102.3592","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3592","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3592v1","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3592","created_at":"2026-05-18T04:28:28Z"},{"alias_kind":"pith_short_12","alias_value":"G6XIRCY3N6LT","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"G6XIRCY3N6LT4GIF","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"G6XIRCY3","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:4e3fc78c29b3d6647ad2f763850b1d1f59e22b7e1492c8fc10d654d62691f6c8","target":"graph","created_at":"2026-05-18T04:28:28Z","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":"Many statistical problems involve mixture models and the need for computationally efficient methods to estimate the mixing distribution has increased dramatically in recent years. Newton [Sankhya Ser. A 64 (2002) 306--322] proposed a fast recursive algorithm for estimating the mixing distribution, which we study as a special case of stochastic approximation (SA). We begin with a review of SA, some recent statistical applications, and the theory necessary for analysis of a SA algorithm, which includes Lyapunov functions and ODE stability theory. Then standard SA results are used to prove consis","authors_text":"Jayanta K. Ghosh, Ryan Martin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-02-17T14:37:43Z","title":"Stochastic Approximation and Newton's Estimate of a Mixing Distribution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3592","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:eb8ac9a6d2495abac9506ea4f66294c49a82dcda572fcf00cfad81c9bde932d5","target":"record","created_at":"2026-05-18T04:28:28Z","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":"57994341ceb1d64349418f79b6d4d69a01bce4cc9d6f547b572f6055a49ec885","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2011-02-17T14:37:43Z","title_canon_sha256":"a5608c4a573467438c1d9ae91958134e84001216c5e649d26c6c57eeec706120"},"schema_version":"1.0","source":{"id":"1102.3592","kind":"arxiv","version":1}},"canonical_sha256":"37ae888b1b6f973e1905d959a427b794909a348711370b69eef44950eead3be4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37ae888b1b6f973e1905d959a427b794909a348711370b69eef44950eead3be4","first_computed_at":"2026-05-18T04:28:28.787346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:28.787346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/6hy5BaMm8/sT/IQbcDt9xbimI70bdE0fL38as0VezWwJnnJQXeBw5zaxofTpg37SXexNOL1p5QtVO5/HXDMAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:28.787738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3592","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb8ac9a6d2495abac9506ea4f66294c49a82dcda572fcf00cfad81c9bde932d5","sha256:4e3fc78c29b3d6647ad2f763850b1d1f59e22b7e1492c8fc10d654d62691f6c8"],"state_sha256":"62b9b0fb190037e7f87a448db67ab98a84f533ebaf6e396ce5c89754ed7f4482"}