Measurement Error Models in Astronomy

Abstract

AbstractI 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.KeywordsMarkov Chain Monte CarloActive Galactic NucleusWeighted Little SquareMarkov Chain Monte Carlo AlgorithmMarkov Chain Monte Carlo SamplerThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.