AI 中文总结
本研究通过信息几何框架分析星系过密度结构在部分天区覆盖下的可推断性，发现连通范围比标量振幅更难恢复，且覆盖机制影响推断结果，单一覆盖比例不足以描述。\n
AI 中文摘要
星系分布的结构统计量通常仅在部分观测的天区上测量，然而，在不完全覆盖下有多少结构得以保留，以及哪些方面最先丢失，很少独立于所报告的统计量进行量化。我们将此问题视为对固定结构向量Theta=(Delta_Omega, f_HD, L_HD)的推断，该向量包含全局密度对比度、高密度区域占比以及高密度集合的连通范围。星系密度通过其Voronoi单元面积分配，连通性基于对偶Delaunay图。两种机制生成子集：空间相关的随机游走覆盖和空间不相关的节点丢失，恢复精度通过一个Fisher启发的参考度量来衡量，该度量在覆盖水平、机制和估计器之间保持固定。应用于包含94043个星系的z切片COSMOS场时，三个分量形成严格层级：在每一个不完全覆盖水平下，连通范围的恢复精度比标量振幅低数倍，且随着覆盖改善差距扩大，并最后收敛。两种机制在相反方向上权衡，均匀丢失保留振幅而随机游走覆盖保留形态，因此可推断性不仅取决于观测了多少天区，还取决于如何观测。一个联合单数准则可以对机制排序，但依赖于容差且可能反转，而分量级对比度与度量无关且稳健；基于度数的逆概率权重虽对随机游走采样自然，但对集合值覆盖不一致。因此，部分场结构统计量在信息空间中各向异性地退化，单一覆盖比例不足以刻画部分观测场能支持的内容。
英文摘要
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.
Comments12 pages, 4 figures. Also archived at Zenodo: https://doi.org/10.5281/zenodo.21551014
