Title: Mitigating Eddington and Malmquist Biases in Latent-Inclination Inference of the Tully-Fisher Relation Show Chinese title

Title: 减轻托勒-费舍尔关系中隐含倾斜推断的爱丁顿和马尔莫奎斯特偏差

Abstract: The Tully-Fisher relation is a vital distance indicator, but its precise inference is challenged by selection bias, statistical bias, and uncertain inclination corrections. This study presents a Bayesian framework that simultaneously addresses these issues. To eliminate the need for individual inclination corrections, inclination is treated as a latent variable with a known probability distribution. To correct for the distance-dependent Malmquist bias arising from sample selection, the model incorporates Gaussian scatter in the dependent variable, the distribution of the independent variable, and the observational selection function into the data likelihood. To mitigate the statistical bias -- termed the ``general Eddington bias'' -- caused by Gaussian scatter and the non-uniform distribution of the independent variable, two methods are introduced: (1) analytical bias corrections applied to the dependent variable before likelihood computation, and (2) a dual-scatter model that accounts for Gaussian scatter in the independent variable within the likelihood function. The effectiveness of these methods is demonstrated using simulated datasets. By rigorously addressing selection and statistical biases in a latent-variable regression analysis, this work provides a robust approach for unbiased distance estimates from standardizable candles, which is critical for improving the accuracy of Hubble constant determinations. Show Chinese abstract

Abstract: TF关系是重要的距离指示器，但其精确推断受到选择偏差、统计偏差和不确定的倾斜校正的挑战。 本研究提出了一种贝叶斯框架，同时解决这些问题。 为了消除对个别倾斜校正的需求，将倾斜视为具有已知概率分布的潜在变量。 为了纠正由于样本选择引起的距离依赖的马尔奎斯特偏差，模型将因变量的高斯散射、自变量的分布和观测选择函数纳入数据似然中。 为了减轻由高斯散射和自变量非均匀分布引起的统计偏差——称为“一般爱丁顿偏差”，引入了两种方法：(1) 在似然计算之前对因变量应用解析偏差校正，(2) 一种双散射模型，在似然函数中考虑自变量的高斯散射。 这些方法的有效性通过模拟数据集进行了演示。 通过在潜在变量回归分析中严格处理选择和统计偏差，这项工作提供了一种从可标准化蜡烛中进行无偏距离估计的稳健方法，这对于提高哈勃常数确定的准确性至关重要。