Accounting for selection biases in population analyses: equivalence of the in-likelihood and post-processing approaches

TL;DR

This paper demonstrates the theoretical equivalence of two methods for correcting selection biases in population analyses, showing that a posteriori correction does not introduce bias if assumptions are met.

Contribution

It proves the equivalence of likelihood-based and post-processing methods for handling selection biases in population studies under certain assumptions.

Findings

The likelihood and post-processing methods are equivalent under specific conditions.

Post-processing correction does not induce bias when assumptions are satisfied.

Theoretical validation of bias correction approaches in population analysis.

Abstract

In this paper I show the equivalence, under appropriate assumptions, of two alternative methods to account for the presence of selection biases (also called selection effects) in population studies: one is to include the selection effects in the likelihood directly; the other follows the procedure of first inferring the observed distribution and then removing selection effects a posteriori. Moreover, I investigate a potential bias allegedly induced by the latter approach: I show that this procedure, if applied under the appropriate assumptions, does not produce the aforementioned bias.