Linear regression is common in astronomical analyses. I discuss a Bayesian hierarchical modelling 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 modelling. The R-package LIRA (LInear Regression in Astronomy) is made available to perform the regression.

Sereno, M. (2016). A Bayesian approach to linear regression in astronomy. MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 455(2), 2149-2162 [10.1093/mnras/stv2374].

A Bayesian approach to linear regression in astronomy

SERENO, MAURO
2016

Abstract

Linear regression is common in astronomical analyses. I discuss a Bayesian hierarchical modelling 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 modelling. The R-package LIRA (LInear Regression in Astronomy) is made available to perform the regression.
2016
Sereno, M. (2016). A Bayesian approach to linear regression in astronomy. MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 455(2), 2149-2162 [10.1093/mnras/stv2374].
Sereno, Mauro
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/589015
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