Pith Number

pith:VNOIYJJL

pith:2026:VNOIYJJLFF5DLNF32C7SIS5TXQ

not attested not anchored not stored refs resolved

A Bayesian Longitudinal Spatial Normative Model for Individualized Brain Deviation Mapping

J. T. Korley

Bayesian longitudinal spatial model reduces brain deviation map reconstruction error by jointly capturing temporal and spatial dependencies.

arxiv:2605.14565 v1 · 2026-05-14 · stat.ME · math.ST · stat.AP · stat.TH

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Claims

C1strongest claim

Across six simulation scenarios and OASIS-3 structural MRI data, the proposed Bayesian longitudinal spatial normative model reduced deviation-map reconstruction error relative to independent cross-sectional and longitudinal non-spatial benchmarks, with RMSE reductions of 54% and 45% respectively in the real data application.

C2weakest assumption

The model assumes that subject-specific deviations can be adequately represented as a latent spatial process whose posterior can be computed under the chosen hierarchical Bayesian specification, with the spatial dependence structure correctly specified for the neuroanatomical data.

C3one line summary

A new Bayesian model jointly models longitudinal and spatial dependencies in brain MRI to produce individualized deviation maps with substantially lower error than independent or non-spatial alternatives.

References

13 extracted · 13 resolved · 0 Pith anchors

[1] Ifτ 2 u = 0, the model reduces to a longitudinal non-spatial normative model

[2] Ifσ 2 b = 0, dependence across regions is induced only through the spatial deviation process

[3] Ifτ 2 u = 0,σ 2 b = 0, andT i = 1for all subjects, the model reduces to an independent cross-sectional regional model. S1

[4] Proof.For part (1), settingτ 2 u = 0implies uir = 0 almost surely for all regions

[5] baseline linear longitudinal structure,

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:05.541963Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab5c8c252b297a35b4bbd0bf244bb3bc1969388bb9522ecab7853113c08992a4

Aliases

arxiv: 2605.14565 · arxiv_version: 2605.14565v1 · doi: 10.48550/arxiv.2605.14565 · pith_short_12: VNOIYJJLFF5D · pith_short_16: VNOIYJJLFF5DLNF3 · pith_short_8: VNOIYJJL

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VNOIYJJLFF5DLNF32C7SIS5TXQ \
  | 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: ab5c8c252b297a35b4bbd0bf244bb3bc1969388bb9522ecab7853113c08992a4

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "f3b091e9aff2fb667f2b647883b213b9fc21f54a768f1ff8cece31830a3179e1",
    "cross_cats_sorted": [
      "math.ST",
      "stat.AP",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-14T08:36:45Z",
    "title_canon_sha256": "6c4bcf76abdfaeeb104713747fdc2d0314adaae2d7c510d62cbf81aa7d41cd13"
  },
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  "source": {
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    "kind": "arxiv",
    "version": 1
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}