  Causal inference in a sub-population involves identifying the causal effect
of an intervention on a specific subgroup, which is distinguished from the
whole population through the influence of systematic biases in the sampling
process. However, ignoring the subtleties introduced by sub-populations can
either lead to erroneous inference or limit the applicability of existing
methods. We introduce and advocate for a causal inference problem in
sub-populations (henceforth called s-ID), in which we merely have access to
observational data of the targeted sub-population (as opposed to the entire
population). Existing inference problems in sub-populations operate on the
premise that the given data distributions originate from the entire population,
thus, cannot tackle the s-ID problem. To address this gap, we provide necessary
and sufficient conditions that must hold in the causal graph for a causal
effect in a sub-population to be identifiable from the observational
distribution of that sub-population. Given these conditions, we present a sound
and complete algorithm for the s-ID problem.
