Pith Number

pith:A7XOYFSF

pith:2025:A7XOYFSFLU6ZIS2YXDVHHMWBSL

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Exact inference via quasi-conjugacy in two-parameter Poisson-Dirichlet hidden Markov models

Dario Span\`o, Marco Dalla Pria, Matteo Ruggiero

A duality with pure-death processes on partitions yields closed-form recursive inference for two-parameter Poisson-Dirichlet hidden Markov models.

arxiv:2512.22098 v4 · 2025-12-26 · stat.ME · math.PR · math.ST · q-bio.PE · stat.CO · stat.TH

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

Receipt and verification

First computed	2026-05-20T00:04:19.535626Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07eeec16455d3d944b58b8ea73b2c192e6891d92a0f0697c5b456fc2e2e9fb73

Aliases

arxiv: 2512.22098 · arxiv_version: 2512.22098v4 · doi: 10.48550/arxiv.2512.22098 · pith_short_12: A7XOYFSFLU6Z · pith_short_16: A7XOYFSFLU6ZIS2Y · pith_short_8: A7XOYFSF

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/A7XOYFSFLU6ZIS2YXDVHHMWBSL \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 07eeec16455d3d944b58b8ea73b2c192e6891d92a0f0697c5b456fc2e2e9fb73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8606a524de1246e201499ef76e1021af8ede91460a2850faf402e884fcca6f5d",
    "cross_cats_sorted": [
      "math.PR",
      "math.ST",
      "q-bio.PE",
      "stat.CO",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2025-12-26T17:54:58Z",
    "title_canon_sha256": "e2b463c8751bd26b4fdf16864047786cf5416565cca07f92dbe77716a7adb7fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.22098",
    "kind": "arxiv",
    "version": 4
  }
}