A unified framework for constructing, tuning and assessing photometric redshift density estimates in a selection bias...

Area of Science:

• Cosmology
• Astrophysics
• Statistical Astronomy

Background:

• Photometric redshift estimation is crucial for precision cosmology.
• Large sky surveys face challenges with selection bias, where bright galaxies differ from fainter ones, impacting redshift accuracy.
• Existing methods often fail for dimmer galaxies due to this bias.

Purpose of the Study:

• To develop a principled framework for photometric redshift probability density function (PDF) estimation.
• To address selection bias and covariate shift inherent in large-scale galaxy surveys.
• To provide methods for tuning, comparing, and combining redshift estimation techniques.

Main Methods:

• Developed a framework for conditional density estimation (photometric redshift PDFs) accounting for selection bias.
• Utilized an assumption that galaxy labeling probability depends only on measured properties, not true redshift.
• Defined risk functions to tune and compare importance weight estimation and conditional density estimation.
• Proposed a method to combine multiple conditional density estimates for improved accuracy.

Main Results:

• Applied the framework to analyze approximately 10^6 galaxies, primarily from the Sloan Digital Sky Survey.
• Demonstrated through diagnostic tests that the method yields accurate conditional density estimates for unlabelled galaxies.
• Successfully addressed the issue of covariate shift induced by selection bias.

Conclusions:

• The proposed framework provides a robust solution for accurate photometric redshift estimation in the presence of selection bias.
• This method enhances the reliability of cosmological studies relying on large galaxy datasets.
• The approach offers improved precision for redshift determination of faint galaxies, crucial for future surveys.