  The most common approach to implementing data analysis pipelines involves
obtaining point estimates from the upstream modules and then treating these as
known quantities when working with the downstream ones. This approach is
straightforward, but it is likely to underestimate the overall uncertainty
associated with any final estimates. An alternative approach involves
estimating parameters from the modules jointly using a Bayesian hierarchical
model, which has the advantage of propagating upstream uncertainty into the
downstream estimates. However, when modules are misspecified, such a joint
model can behave in unexpected ways. Furthermore, hierarchical models require
the development of ad-hoc computational implementations that can be laborious
and computationally expensive. Cut inference modifies the posterior
distribution to prevent information flow between certain parameters and
provides a third alternative for statistical inference in data analysis
pipelines. This paper presents a unified framework that encompasses two-step,
cut, and joint inference in the context of data analysis pipelines with two
modules and uses two examples to illustrate the tradeoffs associated with these
approaches. Our work shows that cut inference provides both some level of
robustness and ease of implementation for data analysis pipelines at a lower
cost in terms of statistical inference.
