Before revision:  Here, I derive a Bayesian agglomerative clustering engine (BACE) for coarse-graining MSMs, making them suitable for extracting human understanding. BACE considerably outperforms existing methods by iteratively lumping together the most kinetically similar states while taking into account model uncertainty.
After revision:  Here, I derive a Bayesian agglomerative clustering engine (BACE) for coarse-graining Markov chains---as well as a more general class of probabilistic models---making them more comprehensible while remaining as faithful as possible to the original kinetics by accounting for model uncertainty.