Pith Number

pith:2RHB4GDL

pith:2026:2RHB4GDL5UVWN3FQC5FTZIXWIK

not attested not anchored not stored refs resolved

Measures of predictive accuracy, miscalibration and discrimination

{\L}ukasz Delong, Mario W\"uthrich

ABC, ABC² and Gini scores rely on predictor-dependent weights that break alignment with mean-consistent loss functions and can produce dishonest model evaluations for point predictions.

arxiv:2605.12679 v1 · 2026-05-12 · stat.ME

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2RHB4GDL5UVWN3FQC5FTZIXWIK}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

ABC, ABC² and Gini scores may lead to dishonest evaluation of point predictions when used for model selection; this gives support to use mean-consistent loss functions as well as the miscalibration and the discrimination measure from the Murphy's decomposition of the expected loss for model evaluation.

C2weakest assumption

That the class of mean-consistent scoring functions is the appropriate reference class for honest evaluation, and that predictor-dependent weights in ABC necessarily violate alignment with this class for all relevant Bregman divergences.

C3one line summary

ABC, ABC squared, and Gini scores for predictive accuracy rely on predictor-dependent weights that misalign with mean-consistent loss functions, supporting instead the miscalibration and discrimination components from Murphy's decomposition.

References

42 extracted · 42 resolved · 0 Pith anchors

[1] Aaberge, R. (2009). Ranking intersecting Lorenz curves. Social Choice and Welfare 33 , 235-259 2009

[2] Atkinson, A. (1969). On the measurement of inequality. Journal of Economic Theory 2 , 244-263 1969

[3] Bendel, R.B., Higgins, S.S., Teberg, J.E., Pyke, D.A. (1989). Comparison of skewness coefficient, coefficient of variation, and Gini coefficient as inequality measures within populations. Oecologia 78 1989

[4] (2025) Gini score under ties and case weights 2025

[5] Dardanoni, V., Lambert, P. (1988). Welfare rankings of income distributions: A role for the variance and some insights for tax reform Social Choice and Welfare 5 , 1-17 1988

Receipt and verification

First computed	2026-05-18T03:09:50.021120Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d44e1e186bed2b66ecb0174b3ca2f642a5d114e323158dfd65fec8ed764d8a52

Aliases

arxiv: 2605.12679 · arxiv_version: 2605.12679v1 · doi: 10.48550/arxiv.2605.12679 · pith_short_12: 2RHB4GDL5UVW · pith_short_16: 2RHB4GDL5UVWN3FQ · pith_short_8: 2RHB4GDL

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/2RHB4GDL5UVWN3FQC5FTZIXWIK \
  | 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: d44e1e186bed2b66ecb0174b3ca2f642a5d114e323158dfd65fec8ed764d8a52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8f129d0654a4a06aca9c3a17f16eaeb3dbc839caa7eb76f9021136b5cfb948f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-05-12T19:29:55Z",
    "title_canon_sha256": "e438f60e38405eaee733eafb066761410ebfaee1f1dd4649c39de7b75a131bad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12679",
    "kind": "arxiv",
    "version": 1
  }
}