When faced with an ambiguous pronoun, an addressee must interpret it by identifying a suitable referent. It has been proposed that the interpretation of pronouns can be captured using Bayes’ Rule: P(referent|pronoun) ∝ P(pronoun|referent)P(referent). This approach has been successful in English and Mandarin Chinese. In this study, we further the cross-linguistic evidence for the Bayesian model by applying it to German personal and demonstrative pronouns, and provide novel quantitative support for the model by assessing model performance in a Bayesian statistical framework that allows implementation of a fully hierarchical structure, providing the most conservative estimates of uncertainty. Data from two story-continuation experiments showed that the Bayesian model overall made more accurate predictions for pronoun interpretation than production and next-mention biases separately. Furthermore, the model accounts for the demonstrative pronoun dieser as well as the personal pronoun, despite the demonstrative having different, and more rigid, resolution preferences.