Probabilistic inference is a key mechanism for reasoning about probabilistic programs. Since exact inference is theoretically expensive, most probabilistic inference systems today have adopted approximate inference techniques, which trade precision for better performance (but often without guarantees). As a result, while desirable for its ultimate precision, the practical effectiveness of exact inference for probabilistic programs is mostly unknown.

This paper presents PSI (http://www.psisolver.org), a novel symbolic analysis system for exact inference in probabilistic programs with both continuous and discrete random variables. PSI computes succinct symbolic representations of the joint posterior distribution represented by a given probabilistic program. PSI can compute answers to various posterior distribution, expectation and assertion queries using its own backend for symbolic reasoning.

Our evaluation shows that PSI is more effective than existing exact inference approaches: (i) it successfully computed a precise result for more programs, and (ii) simplified expressions that existing computer algebra systems (e.g., Mathematica, Maple) fail to handle.