ProPPA: Probabilistic Programming for Stochastic Dynamical Systems

Abstract

Formal languages like process algebras have been shown to be effective tools in modelling a wide range of dynamic systems, providing a high-level description that is readily transformed into an executable model. However, their application is sometimes hampered because the quantitative details of many real-world systems of interest are not fully known. In contrast, in machine learning, there has been work to develop probabilistic programming languages, which provide system descriptions that incorporate uncertainty and leverage advanced statistical techniques to infer unknown parameters from observed data. Unfortunately, current probabilistic programming languages are typically too low-level to be suitable for complex modelling. In this article, we present a Probabilistic Programming Process Algebra (ProPPA), the first instance of the probabilistic programming paradigm being applied to a high-level, formal language, and its supporting tool suite. We explain the semantics of the language in terms of a quantitative generalisation of Constraint Markov Chains and describe the implementation of the language, discussing in some detail the different inference algorithms available and their domain of applicability. We conclude by illustrating the use of the language on simple but non-trivial case studies: here, ProPPA is shown to combine the elegance and simplicity of high-level formal modelling languages with an effective way of incorporating data, making it a promising tool for modelling studies.