  We present a Bayesian approach to machine learning with probabilistic
programs. In our approach, training on available data is implemented as
inference on a hierarchical model. The posterior distribution of model
parameters is then used to \textit{stochastically condition} a complementary
model, such that inference on new data yields the same posterior distribution
of latent parameters corresponding to the new data as inference on a
hierachical model on the combination of both previously available and new data,
at a lower computation cost. We frame the approach as a design pattern of
probabilistic programming referred to herein as `stump and fungus', and
evaluate realization of the pattern on case studies.
