Partial-field inferability of galaxy overdensity structure: An information-geometric account of incomplete sky coverage
Abstract
Structural statistics of the galaxy distribution are routinely measured on only partially observed fields, yet how much structure survives incomplete coverage, and which aspects are lost first, is rarely quantified independently of the statistic being reported. We cast this as inference on a fixed structure vector Theta=(Delta_Omega, f_HD, L_HD): a global density contrast, a high-density fraction, and the connected extent of the high-density set. Densities are assigned to galaxies through their Voronoi cell areas, with connectivity on the dual Delaunay graph. Two mechanisms generate subsets, spatially correlated random-walk coverage and spatially uncorrelated node loss, and recovery is measured with a Fisher-inspired reference metric held fixed across coverage levels, mechanisms and estimators. Applied to a z-sliced COSMOS field of 94043 galaxies, the three components form a strict hierarchy: the connected extent is recovered several times less accurately than the scalar amplitudes at every incomplete coverage, by a margin that widens as coverage improves, and is the last to converge. The two mechanisms trade off in opposite directions, uniform loss preserving the amplitudes and walk coverage the morphology, so inferability depends not only on how much of the field is observed but on how it is observed. A joint single-number criterion can order the mechanisms but is tolerance dependent and can reverse, whereas the component-level contrast is metric-independent and robust; the degree-based inverse-probability weight, though natural for random-walk sampling, is inconsistent for set-valued coverage. Partial-field structure statistics therefore degrade anisotropically in information space, and a single coverage fraction is insufficient to characterise what a partially observed field can support.
Related
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- First-star imprints in a metal-poor galaxy overdensity near the end of reionization
- Rest-frame Ultraviolet Variability of Quasars in the Cosmic Himalayas Overdensity
- SAPPHIRES: A Galaxy Overdensity in the Heart of Cosmic Reionization at z = 8.47
BibTeX
@misc{imbrisak2026partialfield,
title = {{Partial-field inferability of galaxy overdensity structure: An information-geometric account of incomplete sky coverage}},
author = {Marko Imbrišak and Krešimir Tisanić},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26140},
eprint = {2609.26140},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26140},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Partial-field inferability of galaxy overdensity structure: An information-geometric account of incomplete sky coverage
AU - Marko Imbrišak
AU - Krešimir Tisanić
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.26140
UR - https://arxiv.org/abs/2609.26140
AB - Structural statistics of the galaxy distribution are routinely measured on only partially observed fields, yet how much structure survives incomplete coverage, and which aspects are lost first, is rarely quantified independently of the statistic being reported. We cast this as inference on a fixed structure vector Theta=(Delta_Omega, f_HD, L_HD): a global density contrast, a high-density fraction, and the connected extent of the high-density set. Densities are assigned to galaxies through their Voronoi cell areas, with connectivity on the dual Delaunay graph. Two mechanisms generate subsets, spatially correlated random-walk coverage and spatially uncorrelated node loss, and recovery is measured with a Fisher-inspired reference metric held fixed across coverage levels, mechanisms and estimators. Applied to a z-sliced COSMOS field of 94043 galaxies, the three components form a strict hierarchy: the connected extent is recovered several times less accurately than the scalar amplitudes at every incomplete coverage, by a margin that widens as coverage improves, and is the last to converge. The two mechanisms trade off in opposite directions, uniform loss preserving the amplitudes and walk coverage the morphology, so inferability depends not only on how much of the field is observed but on how it is observed. A joint single-number criterion can order the mechanisms but is tolerance dependent and can reverse, whereas the component-level contrast is metric-independent and robust; the degree-based inverse-probability weight, though natural for random-walk sampling, is inconsistent for set-valued coverage. Partial-field structure statistics therefore degrade anisotropically in information space, and a single coverage fraction is insufficient to characterise what a partially observed field can support.
ER -