An Information-based Metric for Observing Strategy Optimization, Demonstrated in the Context of Photometric Redshifts for LSST

Abstract The observing strategy (OS) of an astronomical survey influences the degree to which its resulting data can be used to accomplish any science goal, necessitating upcoming programs, including those on the Rubin and Roman telescopes, to solicit metrics in order to optimally choose an OS balancing the costs and benefits to diverse science cases. The requirement that such metrics must be fast to compute often forces them to bake in analysis choices that may not hold for real data. Furthermore, such metrics do not typically share units, impairing objectivity in combining them in an ultimate decision. We propose a metric for OS optimization that is based on the potentially recoverable mutual information about a physical parameter of interest from a sample of data under the constraints of a realistic OS and present a tractable estimation of a variational lower bound of this mutual information implemented in a public code using conditional normalizing flows. We demonstrate the calculation and interpretation of our information-theoretic metric in the context of photometric redshifts, a data product essential to virtually all extragalactic science applications of the Legacy Survey of Space and Time, using mock galaxy catalogs, showing how it can discriminate between observing strategies that preclude robust redshift constraints and those that preserve more redshift information, without specifying an estimator. As our versatile metric reduces the reliance on analysis choices and is interpretable between science goals, we recommend its use to assess the impact of OS in any science application in which photometry may be forward modeled. ✎