{"paper":{"title":"Exact inference via quasi-conjugacy in two-parameter Poisson-Dirichlet hidden Markov models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A duality with pure-death processes on partitions yields closed-form recursive inference for two-parameter Poisson-Dirichlet hidden Markov models.","cross_cats":["math.PR","math.ST","q-bio.PE","stat.CO","stat.TH"],"primary_cat":"stat.ME","authors_text":"Dario Span\\`o, Marco Dalla Pria, Matteo Ruggiero","submitted_at":"2025-12-26T17:54:58Z","abstract_excerpt":"We introduce a nonparametric model for inferring time-evolving, unobserved probability distributions from discrete-time data consisting of unlabelled partitions. The latent process is a two-parameter Poisson-Dirichlet diffusion, and observations arise via exchangeable sampling. Applications include social and genetic data where only aggregate clustering summaries are observed. To address the intractable likelihood, we develop a tractable inferential framework that avoids label enumeration and direct simulation of the latent state. We exploit a duality between the diffusion and a pure-death pro"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We exploit a duality between the diffusion and a pure-death process on partitions, together with coagulation operators that encode the effect of new data. These yield closed-form, recursive updates for forward and backward inference. We compute exact posterior distributions of the latent state at arbitrary times and predictive distributions of future or interpolated partitions.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The duality between the two-parameter Poisson-Dirichlet diffusion and the pure-death process on partitions, together with the coagulation operators, produces a quasi-conjugate structure that delivers exact closed-form updates without label enumeration or direct state simulation.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Exact posteriors and predictions for two-parameter Poisson-Dirichlet hidden Markov models are obtained via quasi-conjugacy, duality with pure-death processes, and coagulation operators yielding closed-form recursive inference.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A duality with pure-death processes on partitions yields closed-form recursive inference for two-parameter Poisson-Dirichlet hidden Markov models.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"ed55f6365cc61e66a7f3eacf0fb965a06b5dc611325325d658980256c97e9c6b"},"source":{"id":"2512.22098","kind":"arxiv","version":4},"verdict":{"id":"14fbed18-414b-4b79-bb19-a89a86b4b4a2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T19:18:27.997653Z","strongest_claim":"We exploit a duality between the diffusion and a pure-death process on partitions, together with coagulation operators that encode the effect of new data. These yield closed-form, recursive updates for forward and backward inference. We compute exact posterior distributions of the latent state at arbitrary times and predictive distributions of future or interpolated partitions.","one_line_summary":"Exact posteriors and predictions for two-parameter Poisson-Dirichlet hidden Markov models are obtained via quasi-conjugacy, duality with pure-death processes, and coagulation operators yielding closed-form recursive inference.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The duality between the two-parameter Poisson-Dirichlet diffusion and the pure-death process on partitions, together with the coagulation operators, produces a quasi-conjugate structure that delivers exact closed-form updates without label enumeration or direct state simulation.","pith_extraction_headline":"A duality with pure-death processes on partitions yields closed-form recursive inference for two-parameter Poisson-Dirichlet hidden Markov models."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.22098/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}