Identifiability of Bayesian models of perception

Inferring the underlying computational processes from behavioral measurements is a fundamental approach in cognitive science and neuroscience. Although Bayesian decision theory has become a major normative framework for modeling perception and cognition, it is unclear to what extent its modeling components (i.e., prior belief, likelihood function, and loss function) can be recovered from behavioral data. Here, we systematically investigated the problem of inferring such Bayesian models from behavioral tasks. We determined the situations under which some components of Bayesian models are systematically confounded, as well as the practical choices in experimental design that can resolve such ambiguity. Overall, our analytical results guarantee in-principle identifiability under broadly applicable conditions, without any a priori knowledge of prior or encoding. Simulations and applications on the basis of behavioral datasets validate that the predictions of this theory apply in realistic settings. Importantly, our results demonstrate that reliable recovery of the model often requires having data from multiple noise levels. This is a crucial insight that will guide future experimental design.