The sources that emitted the gravitational waves detected by the LIGO and Virgo observatories belong to one or more different astrophysical populations. The properties of the underlying populations, as wells as their number and relative ratios can be inferred using hierarchical Bayesian analysis. The problem is made more challenging by the presence of selection effects, that make some sources easier to observe than others. In this tutorial I will derive the key equations from first principles, and use them in a simple toy problem.