In its full sense, perception rests on an agent's model of how its sensory input comes about and the inferences it draws based on this model. These inferences are necessarily uncertain. Here, we illustrate how the Hierarchical Gaussian Filter (HGF) offers a principled and generic way to deal with the several forms that uncertainty in perception takes. The HGF is a recent derivation of one-step update equations from Bayesian principles that rests on a hierarchical generative model of the environment and its (in)stability. It is computationally highly efficient, allows for online estimates of hidden states, and has found numerous applications to experimental data from human subjects. In this paper, we generalize previous descriptions of the HGF and its account of perceptual uncertainty. First, we explicitly formulate the extension of the HGF's hierarchy to any number of levels; second, we discuss how various forms of uncertainty are accommodated by the minimization of variational free energy as encoded in the update equations; third, we combine the HGF with decision models and demonstrate the inversion of this combination; finally, we report a simulation study that compared four optimization methods for inverting the HGF/decision model combination at different noise levels. These four methods (Nelder–Mead simplex algorithm, Gaussian process-based global optimization, variational Bayes and Markov chain Monte Carlo sampling) all performed well even under considerable noise, with variational Bayes offering the best combination of efficiency and informativeness of inference. Our results demonstrate that the HGF provides a principled, flexible, and efficient—but at the same time intuitive—framework for the resolution of perceptual uncertainty in behaving agents.

Inferring on others' (potentially time-varying) intentions is a fundamental problem during many social transactions. To investigate the underlying mechanisms, we applied computational modeling to behavioral data from an economic game in which 16 pairs of volunteers (randomly assigned to “player” or “adviser” roles) interacted. The player performed a probabilistic reinforcement learning task, receiving information about a binary lottery from a visual pie chart. The adviser, who received more predictive information, issued an additional recommendation. Critically, the game was structured such that the adviser's incentives to provide helpful or misleading information varied in time. Using a meta-Bayesian modeling framework, we found that the players' behavior was best explained by the deployment of hierarchical learning: they inferred upon the volatility of the advisers' intentions in order to optimize their predictions about the validity of their advice. Beyond learning, volatility estimates also affected the trial-by-trial variability of decisions: participants were more likely to rely on their estimates of advice accuracy for making choices when they believed that the adviser's intentions were presently stable. Finally, our model of the players' inference predicted the players' interpersonal reactivity index (IRI) scores, explicit ratings of the advisers' helpfulness and the advisers' self-reports on their chosen strategy. Overall, our results suggest that humans (i) employ hierarchical generative models to infer on the changing intentions of others, (ii) use volatility estimates to inform decision-making in social interactions, and (iii) integrate estimates of advice accuracy with non-social sources of information. The Bayesian framework presented here can quantify individual differences in these mechanisms from simple behavioral readouts and may prove useful in future clinical studies of maladaptive social cognition.