  While Bayesian methods are praised for their ability to incorporate useful
prior knowledge, in practice, convenient priors that allow for computationally
cheap or tractable inference are commonly used. In this paper, we investigate
the following question: for a given model, is it possible to compute an
inference result with any convenient false prior, and afterwards, given any
target prior of interest, quickly transform this result into the target
posterior? A potential solution is to use importance sampling (IS). However, we
demonstrate that IS will fail for many choices of the target prior, depending
on its parametric form and similarity to the false prior. Instead, we propose
prior swapping, a method that leverages the pre-inferred false posterior to
efficiently generate accurate posterior samples under arbitrary target priors.
Prior swapping lets us apply less-costly inference algorithms to certain
models, and incorporate new or updated prior information "post-inference". We
give theoretical guarantees about our method, and demonstrate it empirically on
a number of models and priors.
