From symmetries to stationarity in Markovian Monte Carlo - Balancing flows on loops - Harbander, Vincent (My University, 2026)
Markov chain Monte Carlo (MCMC) algorithms algorithms produce dependent samples of a target distribution. These are used to compute statistics of intractable distributions. A similar theory exists for Markov jump processes called Markovian Monte Carlo (MMC). Research into novel MCMC and MMC algorithms has explored non-reversible alternatives using weaker stationarity conditions than detailed balance. This thesis proves invariance for two new families of kernels belonging to rejection-free, non-reversible MMC algorithms sampling on locally compact Polish groups. The proofs use an unorthodox bottom-up approach. Example implementations of these algorithms are provided in Python.
Keywords: MCMC, MMC, Markov process, Markov chain, Monte Carlo, kernel, group, non-reversible, rejection-free, invariance