Error estimation in astronomy: A guide

TL;DR

This paper provides an accessible overview of various error estimation methods in astronomy, emphasizing their assumptions and applicability for both model-based and independent parameter estimates.

Contribution

It introduces a clear, concise guide to multiple error estimation techniques, including practical approaches for propagating errors through data pipelines.

Findings

Summarizes key error estimation methods like grid search, Fisher matrix, and bootstrapping.

Highlights the importance of error estimates for meaningful scientific parameters.

Provides guidance on propagating measurement errors in complex data pipelines.

Abstract

Estimating errors is a crucial part of any scientific analysis. Whenever a parameter is estimated (model-based or not), an error estimate is necessary. Any parameter estimate that is given without an error estimate is meaningless. Nevertheless, many (undergraduate or graduate) students have to teach such methods for error estimation to themselves when working scientifically for the first time. This manuscript presents an easy-to-understand overview of different methods for error estimation that are applicable to both model-based and model-independent parameter estimates. These methods are not discussed in detail, but their basics are briefly outlined and their assumptions carefully noted. In particular, the methods for error estimation discussed are grid search, varying $\chi^2$, the Fisher matrix, Monte-Carlo methods, error propagation, data resampling, and bootstrapping. Finally, a method is outlined how to propagate measurement errors through complex data-reduction pipelines.