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 recent distance ladder measurements of the Hubble constant \(H_0\). We specifically look for the form of bias in Cepheid selection where the correction depends on the photometric uncertainties, which the data can constrain while simultaneously measuring H0. We find mild evidence for non-zero residual selection corrections for Cepheids within calibrator galaxies at a significance of \(1.3\sigma\) to \(2.3\sigma\) depending on the distance-prior adopted, but find that allowing for them does potentially have an appreciable effect on \(H_0\). Including a single extra parameter to model the unknown cut-off in Cepheid selection in SN Ia host galaxies lowers the recovered \(H_0\) by -1.4km/s/Mpc. Including further selection corrections for the SN Ia samples decreases the recovered \(H_0\) by -0.2km/s/Mpc, while using an equal-volume distance prior rather than one uniform in distance modulus reduces \(H_0\) by -1.0km/s/Mpc. When included together, these effects substantially reduce the inferred tension with CMB measurements.