Probabilistic programming systems generally compute with probability density functions, leaving the base measure of each such function implicit. This usually works, but creates problems in situations where densities with respect to different base measures are accidentally combined or compared. We motivate and clarify the problem in the context of a composable library of probability distributions and bijective transformations. We also propose to solve the problem by standardizing on Hausdorff measure as a base, and by deriving a formula and software architecture for updating densities with respect to Hausdorff measure under diffeomorphic transformations. We hope that by adopting our solution, probabilistic programming systems can become more robust and general, and make a broader class of models accessible to practitioners.

Alexey Radul and Boris Alexeev
*The base measure problem and its solution*

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