A Bayesian approach to linear regression in astronomy

TL;DR

This paper introduces a Bayesian hierarchical model for linear regression in astronomy that accounts for heteroscedastic errors, intrinsic scatter, and evolution over time, improving analysis accuracy.

Contribution

It presents a novel Bayesian hierarchical approach that models time evolution, measurement errors, and biases in astronomical linear regression, with an accompanying R package.

Findings

The method accurately models evolving relationships with redshift.

It effectively addresses measurement errors and selection biases.

Simulations demonstrate improved bias correction over traditional methods.

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.