  We tackle the problem of conditioning probabilistic programs on distributions
of observable variables. Probabilistic programs are usually conditioned on
samples from the joint data distribution, which we refer to as deterministic
conditioning. However, in many real-life scenarios, the observations are given
as marginal distributions, summary statistics, or samplers. Conventional
probabilistic programming systems lack adequate means for modeling and
inference in such scenarios. We propose a generalization of deterministic
conditioning to stochastic conditioning, that is, conditioning on the marginal
distribution of a variable taking a particular form. To this end, we first
define the formal notion of stochastic conditioning and discuss its key
properties. We then show how to perform inference in the presence of stochastic
conditioning. We demonstrate potential usage of stochastic conditioning on
several case studies which involve various kinds of stochastic conditioning and
are difficult to solve otherwise. Although we present stochastic conditioning
in the context of probabilistic programming, our formalization is general and
applicable to other settings.
