Abstract : The last few years have seen several breakthroughs in the semantic foundations of statistical modelling. In this tutorial, I will introduce one of these approaches --- quasi Borel spaces. We will review and develop a semantic tool-kit for measure theory using higher-order functions. We will apply it to the semantic foundations of generative Bayesian modelling.

Keywords : quasi-Borel spaces; Grothendieck quasi-toposes; measure theory; foundations of probability theory; theoretical computer science; probabilistic programming; programming language semantics