Probabilistic Programming Process Algebra

Stochastic processes such as Continuous Time Markov Chains are often used to model natural or engineered systems. A large class of languages, like process algebras, have been developed to formally describe and analyse such systems, but are not applicable when our knowledge of the system is incomplete, as is often the case. On the other hand, the probabilistic programming paradigm is currently receiving much attention as a way of describing probabilistic models and automatically applying sophisticated inference algorithms to match observed behaviour; however, existing languages are not well-suited to dynamical systems. In this talk, I will present ProPPA --- a modelling language incorporating aspects of probabilistic programming into the framework of process algebras. The idea behind the language is to enable the formal description of Markovian stochastic systems with uncertainty, as well as the statistical inference of their parameters based on observed data. I will discuss the implications that introducing uncertainty into the system description has on the syntax and, particularly, the semantics of the language. This is joint work with Jane Hillston and Guido Sanguinetti.