Bayesian changepoint analysis In this thesis we elaborate upon Bayesian changepoint analysis whereby our focus is on three big topics: approximate sampling via MCMC exact inference and uncertainty quantification. Besides modeling matters are discussed in an ongoing fashion. Our findings are underpinned through several changepoint examples with a focus on a well log drilling data. BAYES Markov Kette Statistik Ungewissheit Convergence of Markov chains Highest density regions Integer Linear Program MCMC Model selection NP completeness Perron Frobenius theorem Spike and Slab mixture proposals trans dimensional sampling