论文标题
如何从概率红移估计中获得红移分布
How to obtain the redshift distribution from probabilistic redshift estimates
论文作者
论文摘要
红移分布$ n（z）$的值得信赖的估计对于使用弱重力镜头和银河系目录的大规模结构来研究宇宙学至关重要。预计下一代弱透镜调查的昏暗和众多星系的光谱红移预计将不可用，这使得光度红移（photo-$ z $）概率密度密度函数（PDFS）是次最佳的替代方案，可全面地封装，以影响非trivical囊系统影响照片-UP Z $ Z $ point估算。已建立的堆叠估计器为$ n（z）$避免将照片降低-$ z $ pdfs的点估计，但产生了$ n（z）$的系统偏见估计值，该估计值降低了信号到噪声，这是最必要的，$ z $ pdf是最必要的。 We introduce Cosmological Hierarchical Inference with Probabilistic Photometric Redshifts (CHIPPR), a statistically rigorous probabilistic graphical model of redshift-dependent photometry, which correctly propagates the redshift uncertainty information beyond the best-fit estimator of $n(z)$ produced by traditional procedures and is provably the only self-consistent way to recover $n(z)$ from photo-$z$ PDFS。我们提出$ \ texttt {chippr} $原型代码，并指出数学上合理的方法会产生计算费用。 CHIPPR方法适用于任何随机变量的任何单点统计量，前提是明确已知的先前概率密度。如果先验是隐式的，那么流行的照片 - $ z $技术可能是这种情况，那么所得的后PDF不能用于科学推断。因此，我们建议将照片 - $ z $社区的重点放在开发方法上，以使照片恢复 - $ z $的可能性，并通过直接或通过已知的先前概率密度来支持所有红移。
A trustworthy estimate of the redshift distribution $n(z)$ is crucial for using weak gravitational lensing and large-scale structure of galaxy catalogs to study cosmology. Spectroscopic redshifts for the dim and numerous galaxies of next-generation weak-lensing surveys are expected to be unavailable, making photometric redshift (photo-$z$) probability density functions (PDFs) the next-best alternative for comprehensively encapsulating the nontrivial systematics affecting photo-$z$ point estimation. The established stacked estimator of $n(z)$ avoids reducing photo-$z$ PDFs to point estimates but yields a systematically biased estimate of $n(z)$ that worsens with decreasing signal-to-noise, the very regime where photo-$z$ PDFs are most necessary. We introduce Cosmological Hierarchical Inference with Probabilistic Photometric Redshifts (CHIPPR), a statistically rigorous probabilistic graphical model of redshift-dependent photometry, which correctly propagates the redshift uncertainty information beyond the best-fit estimator of $n(z)$ produced by traditional procedures and is provably the only self-consistent way to recover $n(z)$ from photo-$z$ PDFs. We present the $\texttt{chippr}$ prototype code, noting that the mathematically justifiable approach incurs computational expense. The CHIPPR approach is applicable to any one-point statistic of any random variable, provided the prior probability density used to produce the posteriors is explicitly known; if the prior is implicit, as may be the case for popular photo-$z$ techniques, then the resulting posterior PDFs cannot be used for scientific inference. We therefore recommend that the photo-$z$ community focus on developing methodologies that enable the recovery of photo-$z$ likelihoods with support over all redshifts, either directly or via a known prior probability density.
