Applying Information Theory to Design Optimal Filters for Photometric Redshifts

Abstract

In this paper we apply ideas from information theory to create a method for the design of optimal filters for photometric redshift estimation. We show the method applied to a series of simple example filters in order to motivate an intuition for how photometric redshift estimators respond to the properties of photometric passbands. We then design a realistic set of six filters covering optical wavelengths that optimize photometric redshifts for $z<=2.3$ and $i<25.3$. We create a simulated catalog for these optimal filters and use our filters with a photometric redshift estimation code to show that we can improve the standard deviation of the photometric redshift error by 7.1% overall and improve outliers 9.9% over the standard filters proposed for the Large Synoptic Survey Telescope (LSST). We compare features of our optimal filters to LSST and find that the LSST filters incorporate key features for optimal photometric redshift estimation. Finally, we describe how information theory can be applied to a range of optimization problems in astronomy.

arXiv comment29 pages, 17 figures, accepted to ApJ

References in corpus (13)

• Stellar population synthesis at the resolution of 2003
• LSST: from Science Drivers to Reference Design and Anticipated Data Products
• Measuring and Modelling the Redshift Evolution of Clustering: the Hubble Deep Field North
• Slicing Through Multicolor Space: Galaxy Redshifts From Broadband Photometry
• Information theory in molecular biology
• A comparison of period finding algorithms
• Tracking Dark Energy with the ISW effect: short and long-term predictions
• Photometric Redshifts with the LSST: Evaluating Survey Observing Strategies
• Scientific Synergy Between LSST and Euclid
• Using conditional entropy to identify periodicity
• Entropy-Based Financial Asset Pricing
• Information Gains from Cosmic Microwave Background Experiments
• Robust period estimation using mutual information for multi-band light curves in the synoptic survey era