Measurement Error Models in Astronomy
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.
KeywordsMarkov Chain Monte Carlo Active Galactic Nucleus Weighted Little Square Markov Chain Monte Carlo Algorithm Markov Chain Monte Carlo Sampler
I would like to thank Anca Constantin for sharing her data set with me before publication, and Aneta Siemiginowska, Xiaohui Fan, and Tommaso Treu for helpful comments on an earlier version of this manuscript. I acknowledges support by NASA through Hubble Fellowship grant #HF-51243.01 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555.
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