Abstract
Linear regression is common in astronomical analyses. I discuss a Bayesian
hierarchical modeling of data with heteroscedastic and possibly correlated
measurement errors and intrinsic scatter. The method fully accounts for time
evolution. The slope, the normalization, and the intrinsic scatter of the
relation can evolve with the redshift. The intrinsic distribution of the
independent variable is approximated using a mixture of Gaussian distributions
whose means and standard deviations depend on time. The method can address
scatter in the measured independent variable (a kind of Eddington bias),
selection effects in the response variable (Malmquist bias), and departure from
linearity in form of a knee. I tested the method with toy models and
simulations and quantified the effect of biases and inefficient modeling. The
R-package LIRA (LInear Regression in Astronomy) is made available to perform
the regression.
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