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Description: Intonation plays an integral role in comprehending spoken language. It is also remarkably variable, often exhibiting only probabilistic mappings between form and function. Despite this apparent uncertainty, listeners can rapidly integrate intonational information to predictively map a given pitch accent onto the speaker's likely referential intentions. We use manual response dynamics (mouse-tracking) to investigate two questions: (i) whether listeners draw predictive inferences from the presence and absence of an intonational marking and (ii) whether and how listeners adapt their online interpretation of intonational cues when these are reliable or stochastically unreliable. We formulate a novel Bayesian model of rational predictive cue integration and explore predictions derived under a concrete link hypothesis relating a quantitative notion of evidential strength of a cue to the moment in time, relative to the unfolding speech signal, at which mouse trajectories finally turn towards the eventually selected option. In order to capture rational belief updates after concrete observations of a speaker's behavior, we formulate and explore an extension of this model that includes the listener's hierarchical beliefs about the speaker's likely production behavior. Our results are compatible with the assumption that listeners rapidly and rationally integrate all available intonational information, that they expect reliable intonational information initially, and that they adapt these initial expectations gradually during exposition to unreliable input.