Partial-field inferability of galaxy overdensity structure: An information-geometric account of incomplete sky coverage
Year: 2026
Type: preprint
Abstract: Context. Structural statistics of the galaxy distribution are routinely measured on only partially observed fields. Yet the amount ofstructure that survives incomplete coverage, and which aspects are lost first, is rarely quantified independently of the particular statisticbeing reported.Aims. We cast this question as inference on a fixed structure vector and evaluate recovery with a Fisher-inspired reference metric.From the Voronoi tessellation of a galaxy field, we construct the three-component overdensity structure vector Θ = (ΔΩ, fHD, LHD),comprising a global density contrast, a high-density fraction, and the connected extent of the high-density set. We then ask with whatprobability a subset of the field recovers Θ within a prescribed information tolerance.Methods. We assign local densities to galaxies through their Voronoi cell areas and propagate connectivity on the dual Delaunaygraph. Two mechanisms generate subsets: spatially correlated random-walk coverage and spatially uncorrelated independent nodeloss. Recovery is assessed with a regularised Mahalanobis distance d2g = ΔΘTgΘΔΘ, using a single reference metric estimated oncefrom a stated deviation ensemble and held fixed across coverage levels, mechanisms and estimators. This yields an inferability Hε anda survivability S ε that can be compared at matched coverage. We apply the analysis to a z-sliced COSMOS field containing 94 043galaxies.Results. The three components form a strict hierarchy. At every incomplete coverage we sample, the connected extent LHD is recoveredseveral times less accurately than the scalar components, by a margin that widens as coverage improves, and it is the last to converge.The two subset mechanisms trade off in opposite directions: uniform loss preserves the scalar amplitudes more accurately, whereaswalk coverage better preserves morphology. Inferability therefore depends not only on how much of the field is observed, but also onhow it is observed. A joint criterion combining the three components can order the two mechanisms at matched coverage, but thatsingle-number ordering is tolerance dependent and can reverse, whereas the component-level contrast is independent of the metric androbust. We further show that the degree-based inverse-probability weight, although natural for random-walk sampling, is inconsistentfor set-valued coverage and leaves a bias that does not vanish even at complete coverage.Conclusions. Partial-field structure statistics therefore degrade anisotropically in information space: scalar amplitudes survive samplingthat destroys connectivity, and connectivity survives sampling that biases amplitudes. A single coverage fraction is thus insufficientto characterise what a partially observed field can support.
Source: arXiv (Cornell University)
Authors: Imbrišak, Marko, Tisanić, Krešimir
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7171159366