My research interest lie in computational statistics and simulation algorithms with particular focus on unbiased and exact estimation and their use in reliable statistical inference. The central aspect of this is algorithmic processing of randomness and developing a calculus of random variables that would allow to use random objects that can be simulated on a computer, but that have no known closed form mathematical formula describing them. Developing the approach, which is the theme of my Royal Society University Research Fellowship, will enable reliable inference for otherwise intractable complex models in modern statistics.