Mitigating Eddington and Malmquist Biases in Latent-Inclination Regression of the Tully-Fisher Relation

Precise estimation of the Tully-Fisher relation is compromised by statistical biases and uncertain inclination corrections. To account for selection effects (Malmquist bias) while avoiding individual inclination corrections, I introduce a Bayesian method based on likelihood functions that incorporate Sine-distributed scatter of rotation velocities, Gaussian scatter from intrinsic dispersion and measurement error, and the observational selection function. However, tests of unidirectional models on simulated datasets reveal an additional bias arising from neglect of the Gaussian scatter in the independent variable. This additional bias is identified as a generalized Eddington bias, which distorts the data distribution independently of Malmuqist bias. I introduce two extensions to the Bayesian method that successfully mitigate the Eddington bias: (1) analytical bias corrections of the dependent variable prior to likelihood computation, and (2) a bidirectional dual-scatter model that includes the Gaussian scatter of the independent variable in the likelihood function. By rigorously accounting for Malmquist and Eddington biases in a latent-inclination regression analysis, this work establishes a framework for unbiased distance estimates from standardizable candles, critical for improving determinations of the Hubble constant.