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

TL;DR

This paper highlights the limitations of current nonparametric methods in astronomy, offering a guide for selecting optimal techniques and providing a Python library with new and existing algorithms to improve data efficiency.

Contribution

It introduces a practical guide for astronomers to choose suitable nonparametric regression methods and provides a Python library with both existing and novel algorithms.

Findings

Identifies flaws in common nonparametric techniques

Provides a decision guide for method selection

Develops and releases new algorithms in Python

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.