bachelor’s thesis, university of edinburgh, 2021
l. g. stigliano, a. teckentrup
this project gives a comprehensive introduction to inverse problems and markov chain monte carlo methods. we begin by introducing inverse problems and how to solve them, focusing on the bayesian inference approach. we then argue for the value in using markov chain monte carlo methods within this approach, shifting focus onto these methods.
we first introduce markov chains to give the reader appropriate background for the theory behind these methods, then turn to markov chain monte carlo methods, in particular the metropolis–hastings algorithm. subsequently, we propose a different class of methods called non-reversible samplers, which have highly desirable theoretical properties. we compare the performance of these different algorithms in a series of illustrative examples, and conclude by applying them to inverse problems in imaging.