The Identifiability of Bayesian Models of Perceptual Decision

Introduction: Inferring the underlying computational processes from behavioral measurements represents a fundamental approach in psychology, neuroscience, and cognitive science. This problem may be ill-posed in that different neural processes and implementations can give rise to the same behavior. In perceptual science, an important normative modeling framework is the Bayesian observer model, which models perceptual decisions in terms of the likelihood function, the prior belief, and the loss function. Surprisingly, it remains unclear to what extent these modeling components can be recovered from behavioral data. Method: Using a combination of theory, numerical simulation, and analysis of behavioral data, we systematically investigate the problem of inferring components of Bayesian observer models from psychophysical tasks, including both continuous estimation and two-alternative forced choice (2AFC) tasks. Results: Our theoretical results guarantee in-principle identifiability under broadly applicable conditions, without any a priori knowledge of the prior distribution or stimulus encoding. In particular, when the loss function is known, the prior and encoding can be systematically identified. Interestingly, prior and loss function can be systematically confounded when the loss function is unknown. Importantly, this can be resolved by having behavioral responses based on multiple noise levels. We also find that identifiability can be achieved through the manipulation of either internal noise or stimulus noise. Numerical simulations and applications based on published behavioral datasets validate that the predictions of this theory apply in realistic settings. Conclusion: Our work leads to a systematic characterization of the identifiability of a large family of Bayesian observer models. Crucially, our results demonstrated that reliable recovery of the model components often requires having data from multiple noise levels. Our results have broad implications in interpreting existing data and in designing future psychophysical experiments.