Pith Number

pith:RKERWF2U

pith:2026:RKERWF2UZXYDUAETCQAGJ46DKO

not attested not anchored not stored refs resolved

Global structure of the time delay likelihood

Namu Kroupa, Will Handley

The likelihood for time delay inference develops a generic boundary-driven W-shape with a global maximum at the true delay.

arxiv:2602.22307 v3 · 2026-02-25 · stat.ME · astro-ph.CO · astro-ph.GA · astro-ph.IM

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Claims

C1strongest claim

By analysing the likelihood for time delay inference with Gaussian process light curve models, we show that it generically develops a boundary-driven 'W'-shape with a global maximum at the true delay and gradual rises towards the edges of the observation window.

C2weakest assumption

That the Gaussian process light curve models used in the simulations are sufficiently representative of real astronomical data and that the extrapolative boundary effects observed will dominate over other systematics in practice.

C3one line summary

Time delay likelihoods modeled with Gaussian processes develop a boundary-driven W-shape with a global maximum at the true delay and rises at observation window edges, misleading nested sampling and biasing H0 high.

References

93 extracted · 93 resolved · 5 Pith anchors

[1] Therefore, the data-averaged like- lihood may be larger at any time delay, in particular at the boundary

[2] If σis comparable toAor larger,y 1 andy 2 lose their mu- tual correlation, which does not align with the real data sets considered here

[3] This error propagates to the numerical value of the likelihood itself

[4] More generally, non-stationary GPs with non-constant mean functions can extrapolate trends and we could expect that the problem with the drift disap- pears

[5] for each light curve, we subtract the mean and divide the magni- tudes by the standard deviation 2000

Receipt and verification

First computed	2026-05-20T00:05:42.596663Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8a891b1754cdf03a0093140064f3c353839ec81316ae0bdc3f2fd9dcbd8b6b3d

Aliases

arxiv: 2602.22307 · arxiv_version: 2602.22307v3 · doi: 10.48550/arxiv.2602.22307 · pith_short_12: RKERWF2UZXYD · pith_short_16: RKERWF2UZXYDUAET · pith_short_8: RKERWF2U

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RKERWF2UZXYDUAETCQAGJ46DKO \
  | 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: 8a891b1754cdf03a0093140064f3c353839ec81316ae0bdc3f2fd9dcbd8b6b3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "12e2c8f68fa3662aaa52fb6f2fda7d51d2b82e1520fc368882bdc5810ccf6bcd",
    "cross_cats_sorted": [
      "astro-ph.CO",
      "astro-ph.GA",
      "astro-ph.IM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ME",
    "submitted_at": "2026-02-25T19:00:00Z",
    "title_canon_sha256": "6b1066545fc0931467855e15b5dd7df9fec59035032a54c6d0f3861daaa8402c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.22307",
    "kind": "arxiv",
    "version": 3
  }
}