Nonparametric Methods in Astronomy: Think, Regress, Observe -- Pick Any Three

Abstract

Telescopes are much more expensive than astronomers, so it is essential to minimize required sample sizes by using the most data-efficient statistical methods possible. However, the most commonly used model-independent techniques for finding the relationship between two variables in astronomy are flawed. In the worst case they can lead without warning to subtly yet catastrophically wrong results, and even in the best case they require more data than necessary. Unfortunately, there is no single best technique for nonparametric regression. Instead, we provide a guide for how astronomers can choose the best method for their specific problem and provide a python library with both wrappers for the most useful existing algorithms and implementations of two new algorithms developed here.

arXiv comment19 pages, PASP

References in corpus (15)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• A Catalog of Quasar Properties from SDSS DR7
• Fast and scalable Gaussian process modeling with applications to astronomical time series
• The Sloan Digital Sky Survey Quasar Catalog V. Seventh Data Release
• Systematic Errors in Future Weak Lensing Surveys: Requirements and Prospects for Self-Calibration
• The Environment of AGNs in the Sloan Digital Sky Survey
• Mapping the Galaxy Color-Redshift Relation: Optimal Photometric Redshift Calibration Strategies for Cosmology Surveys
• Extreme deconvolution: Inferring complete distribution functions from noisy, heterogeneous and incomplete observations
• Radial-Velocity Fitting Challenge. II. First results of the analysis of the data set
• The Quasar Mass-Luminosity Plane I: A Sub-Eddington Limit for Quasars
• The Distribution of AGN in Clusters of Galaxies
• The Origin of the Spatial Distribution of X-ray luminous AGN in Massive Galaxy Clusters
• Environmental dependence of AGN activity in the supercluster A901/2
• Changing Ionization Conditions in SDSS Galaxies with AGN as a Function of Environment from Pairs to Clusters

Cited by in corpus (6)

• The MUSE-Wide Survey: A determination of the Lyman $\alpha$ emitter luminosity function at $3<z<6$
• COSMOGRAIL XVII: Time delays for the quadruply imaged quasar PG 1115+080
• Effects of Supernova Redshift Uncertainties on the Determination of Cosmological Parameters
• COSMOS2020: Manifold Learning to Estimate Physical Parameters in Large Galaxy Surveys
• Revising the Giant Planet Mass-Metallicity Relation: Deciphering the Formation Sequence of Giant Planets
• Reconstruction of late-time cosmology using Principal Component Analysis