What You Don't Know Won't Hurt You: Self-Consistent Hierarchical Inference with Unknown Follow-up Selection Strategies

TL;DR

This paper presents a hierarchical Bayesian method that allows accurate inference of astrophysical source populations without explicitly modeling complex follow-up selection processes.

Contribution

It demonstrates that self-consistent population inference is possible even with unmodeled, correlated follow-up decisions, simplifying analysis of large survey data.

Findings

Population parameters can be accurately inferred without modeling follow-up decisions.

Follow-up process impacts the precision of posterior constraints.

Contaminant populations may need to be modeled if initial selection is imperfect.

Abstract

Many astronomical surveys prompt follow-up observations, but the decision process through which candidates are selected for follow-up can be difficult to model. This poses a challenge when inferring properties of the intrinsic population of astrophysical sources, rather than those of the set of objects detected by the survey and often-incomplete follow-up observations. We alleviate this problem by demonstrating that explicitly modeling of the follow-up selection process is not required for self-consistent inference of the intrinsic population. Using the framework of hierarchical Bayesian inference, we show that the intrinsic population can be accurately inferred even when the decision to follow up candidates strongly correlates with latent parameters of interest. We provide several worked examples, showing that the precision of posterior constraints can depend on the follow-up process and that one may have to model a population of contaminants if the initial selection is imperfect. Our result could dramatically simplify population inference that incorporates uncoordinated follow-up from multiple observers triggered by the deluge of candidates from surveys like LSST, Gaia, and next-generation gravitational-wave interferometers.