Licentiate seminar in mathematical statistics, Ruben Seyer

Faculty opponent: Jun Yang, University of Copenhagen

Abstract: Bayesian computation with Markov processes is a cornerstone of modern statistical inference, enabling scientists and engineers to reason about uncertainty in large, complex models across fields from physics and biology to finance and artificial intelligence. An important tool for simulation in these models is Markovian Monte Carlo, where the next sample is generated based only on the current one. This allows the estimation of quantities of interest for Bayesian inference in an asymptotically exact manner. This thesis is based on two papers within sampling with Markovian Monte Carlo methods: The first appended paper introduces a gradient estimator based on coupled simulation of samplers. Even though the output of these samplers generally does not depend smoothly on the target distribution, the gradient can consistently be estimated using the difference between carefully coupled samplers, providing an approach to problems in sensitivity analysis and optimisation over sampler output. The second appended paper introduces a framework for constructing non-reversible samplers. Classical methods are generally reversible, which risks slowing down exploration of the target distribution due to diffusive behaviour. By breaking reversibility through an appropriate symmetry of the process, we obtain samplers that are more robust to the choice of tuning parameters.