Measurement errors and scaling relations in astrophysics: a review
  This review article considers some of the most common methods used in
astronomy for regressing one quantity against another in order to estimate the
model parameters or to predict an observationally expensive quantity using
trends between object values. These methods have to tackle some of the awkward
features prevalent in astronomical data, namely heteroscedastic
(point-dependent) errors, intrinsic scatter, non-ignorable data collection and
selection effects, data structure and non-uniform population (often called
Malmquist bias), non-Gaussian data, outliers and mixtures of regressions. We
outline how least square fits, weighted least squares methods, Maximum
Likelihood, survival analysis, and Bayesian methods have been applied in the
astrophysics literature when one or more of these features is present. In
particular we concentrate on errors-in-variables regression and we advocate
Bayesian techniques.
