{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:DSUU3G6YOGFHMGCJL4QWAPLVFM","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":"e09796ac48e60fb4db430bbe9d5900f6b3d932902bbdbedcc2285b197f0294a4","cross_cats_sorted":["math.ST","stat.OT","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.CO","submitted_at":"2023-12-08T08:29:47Z","title_canon_sha256":"1732d9251e6167326e365d22924bdc744419cf7eea822b22317118c5bcb6b6f5"},"schema_version":"1.0","source":{"id":"2312.04898","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.04898","created_at":"2026-07-05T09:44:06Z"},{"alias_kind":"arxiv_version","alias_value":"2312.04898v2","created_at":"2026-07-05T09:44:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.04898","created_at":"2026-07-05T09:44:06Z"},{"alias_kind":"pith_short_12","alias_value":"DSUU3G6YOGFH","created_at":"2026-07-05T09:44:06Z"},{"alias_kind":"pith_short_16","alias_value":"DSUU3G6YOGFHMGCJ","created_at":"2026-07-05T09:44:06Z"},{"alias_kind":"pith_short_8","alias_value":"DSUU3G6Y","created_at":"2026-07-05T09:44:06Z"}],"graph_snapshots":[{"event_id":"sha256:a3c60cf67d64da509fd2eae28c7b4b6f61885d82f439ef4b1ee330d0738a5c24","target":"graph","created_at":"2026-07-05T09:44:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2312.04898/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study linear preconditioning in Markov chain Monte Carlo. We consider the class of well-conditioned distributions, for which several mixing time bounds depend on the condition number $\\kappa$. First we show that well-conditioned distributions exist for which $\\kappa$ can be arbitrarily large and yet no linear preconditioner can reduce it. We then impose two sets of extra assumptions under which a linear preconditioner can significantly reduce $\\kappa$. For the random walk Metropolis we further provide upper and lower bounds on the spectral gap with tight $1/\\kappa$ dependence. This allows u","authors_text":"Max Hird, Samuel Livingstone","cross_cats":["math.ST","stat.OT","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.CO","submitted_at":"2023-12-08T08:29:47Z","title":"Quantifying the effectiveness of linear preconditioning in Markov chain Monte Carlo"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.04898","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":"sha256:75bc6d225b3a15828f03c306fbe3020c04abcc29c4d9e4f4d3f5ae5e0621bfcd","target":"record","created_at":"2026-07-05T09:44:06Z","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":"e09796ac48e60fb4db430bbe9d5900f6b3d932902bbdbedcc2285b197f0294a4","cross_cats_sorted":["math.ST","stat.OT","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.CO","submitted_at":"2023-12-08T08:29:47Z","title_canon_sha256":"1732d9251e6167326e365d22924bdc744419cf7eea822b22317118c5bcb6b6f5"},"schema_version":"1.0","source":{"id":"2312.04898","kind":"arxiv","version":2}},"canonical_sha256":"1ca94d9bd8718a7618495f21603d752b30c8a17e4aa4e547f6ea09a3bc283979","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ca94d9bd8718a7618495f21603d752b30c8a17e4aa4e547f6ea09a3bc283979","first_computed_at":"2026-07-05T09:44:06.329141Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:44:06.329141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hXH5r1p62pwz598QtqfB8DBpXEp0hams4nNLNViEevhFzHZSs634okxRnVkJhKYWBoLrtUKADXv0FJ3czMNlDA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:44:06.329619Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.04898","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75bc6d225b3a15828f03c306fbe3020c04abcc29c4d9e4f4d3f5ae5e0621bfcd","sha256:a3c60cf67d64da509fd2eae28c7b4b6f61885d82f439ef4b1ee330d0738a5c24"],"state_sha256":"bef2687b05afe7f84c5d73eccef7792853ca22f641f3a62fb548b7651a55728d"}