Selection effects in correlated observations with application to distance-ladder observations

For over a century, following the work of Eddington, Kapteyn, Malmquist and others, astronomers have wrestled with selection biases when making inferences from samples of objects. Typically, selection is performed on the same observations used to make the measurements of interest. However, selecting objects using one observable while analyzing another can also lead to a selection bias when the observables are correlated. Within a Bayesian framework, unmodelled selection effects correspond to a misspecified generative model. We derive the likelihood for truncated selection in correlated observables and demonstrate its usefulness by searching for residual selection effects of this form in Cepheid variable star brightness measurements used in recent distance-ladder measurements of the Hubble constant H0. We specifically look for the form of bias where the selection correction depends on the photometric uncertainties, which the Cepheid data can constrain while simultaneously measuring H0. We find only weak evidence for non-zero residual selection corrections, at a significance of (1.2sigma) to (1.9sigma), depending on the distance prior adopted. Including a single extra parameter to model the unknown cut-off lowers the recovered H0 by-0.7km/s/Mpc to-1.1km/s/Mpc, again depending on the distance prior. Allowing for a different selection for each host galaxy can decrease H0 further, although this becomes very sensitive to the distance prior applied. While introducing a new selection correction cannot by itself explain the Hubble tension, it may be a component of a multi-faceted solution that includes the choice of priors on distances and other effects.