Pith Number

pith:CH5QOPMF

pith:2025:CH5QOPMFGAZIZDYFUW7BAVVRSE

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Detecting Model Misspecification in Bayesian Inverse Problems via Variational Gradient Descent

Andrew Curtis, Chris. J. Oates, Katherine Tant, Matthew A. Fisher, Qingyang Liu, Xuebin Zhao, Zheyang Shen

Comparing the standard Bayesian posterior to a predictively oriented mixing distribution detects model misspecification.

arxiv:2512.01667 v3 · 2025-12-01 · stat.ME · stat.CO

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Claims

C1strongest claim

Our contribution is to demonstrate that one can empirically detect model misspecification by comparing the standard Bayesian posterior to the PrO `posterior' Q. To operationalise this, we present an efficient numerical algorithm based on variational gradient descent.

C2weakest assumption

In the well-specified setting one expects the mixing distribution Q to concentrate around the true data-generating parameter in the large data limit, while such singular concentration will typically not be observed if the model is misspecified.

C3one line summary

Comparing the standard Bayesian posterior to a predictive-oriented mixture posterior Q fitted via variational gradient descent detects model misspecification in inverse problems.

Formal links

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Cited by

1 paper in Pith

Concentration and Calibration in Predictive Bayesian Inference

Receipt and verification

First computed	2026-06-08T01:03:52.142490Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11fb073d8530328c8f05a5be1056b191335317ae1ad2398b082357545fe657d6

Aliases

arxiv: 2512.01667 · arxiv_version: 2512.01667v3 · doi: 10.48550/arxiv.2512.01667 · pith_short_12: CH5QOPMFGAZI · pith_short_16: CH5QOPMFGAZIZDYF · pith_short_8: CH5QOPMF

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/CH5QOPMFGAZIZDYFUW7BAVVRSE \
  | 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: 11fb073d8530328c8f05a5be1056b191335317ae1ad2398b082357545fe657d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36615da1b9e34a95c41aafe10ffc824f50c54de3e6971cccdd66a0987ef4201c",
    "cross_cats_sorted": [
      "stat.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2025-12-01T13:37:02Z",
    "title_canon_sha256": "962836fbc34a32b21c54f66e709542b511b161b68dc6bcf5096b908fddae0031"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.01667",
    "kind": "arxiv",
    "version": 3
  }
}