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

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.