Measurement Error Models in Astronomy

TL;DR

This paper reviews statistical methods for correcting measurement errors in astronomical data analysis, focusing on regression and density estimation, and demonstrates Bayesian application to real data with large errors.

Contribution

It provides a comprehensive review of functional and structural models for measurement error correction, emphasizing recent methods like moments, maximum-likelihood, and Bayesian approaches.

Findings

Bayesian analysis effectively handles large measurement errors.

Structural models improve regression accuracy in noisy data.

Discussion of advantages and disadvantages of various methods.

Abstract

I discuss the effects of measurement error on regression and density estimation. I review the statistical methods that have been developed to correct for measurement error that are most popular in astronomical data analysis, discussing their advantages and disadvantages. I describe functional models for accounting for measurement error in regression, with emphasis on the methods of moments approach and the modified loss function approach. I then describe structural models for accounting for measurement error in regression and density estimation, with emphasis on maximum-likelihood and Bayesian methods. As an example of a Bayesian application, I analyze an astronomical data set subject to large measurement errors and a non-linear dependence between the response and covariate. I conclude with some directions for future research.