Measurement Error Models in Astronomy

Details Measurement Error Models in Astronomy Measurement Error Models in Astronomy

2011-12-08

arxiv.org/abs/1112.1745v1

Astronomy and Astrophysics

Astrophysics

Instrumentation and Methods for Astrophysics

15 pages, 2 figures, review based on invited talk at "Statistical Challenges in Modern Astronomy V", held at Penn State in Jun

Scientific paper

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.

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