Forward-modelling Milky Way Cepheids: selection effects and physical priors in the Gaia-HST calibration

TL;DR

This paper presents a Bayesian framework for calibrating Milky Way Cepheids using Gaia data, explicitly modeling selection effects and Galactic structure to improve the local distance ladder and Hubble constant estimates.

Contribution

It introduces a fully forward-modelled Bayesian approach that accounts for selection functions and Galactic geometry in Cepheid calibration, reducing biases in the period-luminosity relation.

Findings

Bayesian modeling yields period-luminosity parameters consistent with previous estimates.

Ignoring selection effects biases the zero-point by about 0.05 mag.

Self-consistent modeling supports the robustness of the local H_0 measurement.

Abstract

The advent of high-precision Gaia parallaxes for Milky Way Cepheids enables per cent-level calibration of the local distance ladder and $H_0$. We revisit the Milky Way Cepheid calibration from Gaia EDR3 parallaxes using a fully forward-modelled Bayesian framework that simultaneously infers the period--luminosity relation, the Gaia parallax zero-point offset, and individual stellar distances while explicitly incorporating the disk geometry of the Galaxy through the distance prior and the selection functions specified in two distinct HST SH0ES campaigns. We derive an analytic treatment of the detection probability that accounts for magnitude, parallax, period, and extinction cuts and reduces the selection treatment to a tractable integral over distance and sky position. Posterior predictive checks show that this generative model matches well the observed distributions of parallaxes, magnitudes, and periods. Modelling Galactic structure and survey truncation self-consistently in a Bayesian framework yields period--luminosity parameters that agree with the SH0ES maximum-likelihood values at the ${<}0.5\,\sigma$ level, a consequence, we show, of the small intrinsic scatter of the Cepheid period--luminosity relation. Adopting, as recently advocated, a uniform-in-volume prior without simultaneously accounting for selection leads to a ${\sim}\,0.05~\mathrm{mag}$ bias in the period--luminosity zero-point and posterior predictive distributions incompatible with the observed data; this shift is mostly driven by the omission of the selection model. A consistent Bayesian treatment of Galactic structure and selection effects reinforces the local distance-ladder determination of $H_0$, and hence the Hubble tension with early-Universe inferences.