The precision of multisensory perception improves when cues arising from the same cause are integrated, such as visual and vestibular heading cues for an observer moving through a stationary environment. In order to determine how the cues should be processed, the brain must infer the causal relationship underlying the multisensory cues. In heading perception, however, it is unclear whether observers follow the Bayesian strategy, a simpler non-Bayesian heuristic, or even perform causal inference at all. We developed an efficient and robust computational framework to perform Bayesian model comparison of causal inference strategies, which incorporates a number of alternative assumptions about the observers. With this framework, we investigated whether human observers' performance in an explicit cause attribution and an implicit heading discrimination task can be modeled as a causal inference process. In the explicit causal inference task, all subjects accounted for cue disparity when reporting judgments of common cause, although not necessarily all in a Bayesian fashion. By contrast, but in agreement with previous findings, data from the heading discrimination task only could not rule out that several of the same observers were adopting a forced-fusion strategy, whereby cues are integrated regardless of disparity. Only when we combined evidence from both tasks we were able to rule out forced-fusion in the heading discrimination task. Crucially, findings were robust across a number of variants of models and analyses. Our results demonstrate that our proposed computational framework allows researchers to ask complex questions within a rigorous Bayesian framework that accounts for parameter and model uncertainty.