Better Languages for Statistics: foundations for non-parametric probabilistic programming

Probabilistic programming is a powerful method for Bayesian statistical modelling, particularly where the sample space is complex or unbounded (non-parametric). This is because the statistical model can be described clearly in a way that is precise but separate from inference algorithms. It accommodates complex models in such a way that outcomes are still explainable.The objective of the proposed research is to develop a semantic foundation for probabilistic programming that properly explains the non-parametric aspects, particularly the symmetries that arise there. There are three ultimate goals:* to propose new probabilistic programming languages: better languages for statistics;* to devise new general inference methods for probabilistic programs;* to build new foundations for probability.The method is to build on advances on exploiting symmetries in traditional programming lan- guage semantics, by combining this with recent successes in formal semantics and verification for probabilistic programming.