  We derive a Bayesian framework for incorporating selection effects into
population analyses. We allow for both measurement uncertainty in individual
measurements and, crucially, for selection biases on the population of
measurements, and show how to extract the parameters of the underlying
distribution based on a set of observations sampled from this distribution. We
illustrate the performance of this framework with an example from
gravitational-wave astrophysics, demonstrating that the mass ratio distribution
of merging compact-object binaries can be extracted from Malmquist-biased
observations with substantial measurement uncertainty.
