Computational modelling is changing the face of science. Many complex systems can be understood as embodied computational systems performing distributed computations on a massive scale. Biology is the discipline where these ideas find their most natural application: cells can be viewed as input/ output devices, with proteins and organelles behaving as finite state machines performing distributed computations inside the cell. This led to the influential framework of cell as computation, and the successful deployment of formal verification and analysis on models of biological systems.This paradigm shift in our understanding of biology has been possible due to the increasingly quantitative experimental techniques being developed in experimental biology. Formal modelling techniques, however, do not have mechanisms to directly include the information obtained from experimental observations in a statistically consistent way. This difficulty in relating the experimental and theoretical developments in biology is a central problem: without incorporating observations, it is extremely difficult to obtain reliable parametrisations of models. More importantly, it is impossible to assess the confidence of model predictions. This means that the central scientific task of falsifying hypotheses cannot be performed in a statistically meaningful way, and that it is very difficult to employ model predictions to rationally plan novel experiments.In this project we will build and develop machine learning tools for continuous time stochastic processes to obtain a principled treatment of the uncertainty at every step of the modelling pipeline. We will use and extend probabilistic programming languages to fully automate the inference tasks, and link to advanced modelling languages to allow formal analysis tools to be deployed in a data modelling framework. We will pursue twoapplications to fundamental problems in systems biology, guaranteeing impact on exciting scientific questions.