Preprint
Mitigating Eddington and Malmquist Biases in Latent-Inclination Regression of the Tully-Fisher Relation
ArXiV.org
Cornell University
04/14/2025
DOI: 10.48550/arxiv.2504.10589
Abstract
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.
Details
- Title: Subtitle
- Mitigating Eddington and Malmquist Biases in Latent-Inclination Regression of the Tully-Fisher Relation
- Creators
- Hai Fu
- Resource Type
- Preprint
- Publication Details
- ArXiV.org
- DOI
- 10.48550/arxiv.2504.10589
- ISSN
- 2331-8422
- Publisher
- Cornell University; Ithaca, New York
- Language
- English
- Date posted
- 04/14/2025
- Academic Unit
- Physics and Astronomy
- Record Identifier
- 9984811208602771
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