2011/12/08 by Kelly, Brandon C.
#Data Analysis #FOS: Physical sciences #Instrumentation and Methods for Astrophysics (astro-ph.IM) #Statistics and Probability (physics.data-an)
paper · doi:10.48550/arxiv.1112.1745
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.