Two theoretical ideas have emerged recently with the ambition to provide a unifying functional explanation of neural population coding and dynamics: predictive coding and Bayesian inference. Here, we describe the two theories and their combination into a single framework: Bayesian predictive coding. We clarify how the two theories can be distinguished, despite sharing core computational concepts and addressing an overlapping set of empirical phenomena. We argue that predictive coding is an algorithmic / representational motif that can serve several different computational goals of which Bayesian inference is but one. Conversely, while Bayesian inference can utilize predictive coding, it can also be realized by a variety of other representations. We critically evaluate the experimental evidence supporting Bayesian predictive coding and discuss how to test it more directly.

Humans stand out from other animals in that they are able to explicitly report on the reliability of their internal operations. This ability, which is known as metacognition, is typically studied by asking people to report their confidence in the correctness of some decision. However, the computations underlying confidence reports remain unclear. In this paper, we present a fully Bayesian method for directly comparing models of confidence. Using a visual two-interval forced-choice task, we tested whether confidence reports reflect heuristic computations (e.g. the magnitude of sensory data) or Bayes optimal ones (i.e. how likely a decision is to be correct given the sensory data). In a standard design in which subjects were first asked to make a decision, and only then gave their confidence, subjects were mostly Bayes optimal. In contrast, in a less-commonly used design in which subjects indicated their confidence and decision simultaneously, they were roughly equally likely to use the Bayes optimal strategy or to use a heuristic but suboptimal strategy. Our results suggest that, while people’s confidence reports can reflect Bayes optimal computations, even a small unusual twist or additional element of complexity can prevent optimality.

European governments use non-pharmaceutical interventions (NPIs) to control resurging waves of COVID-19. However, they only have outdated estimates for how effective individual NPIs were in the first wave. We estimate the effectiveness of 17 NPIs in Europe’s second wave from subnational case and death data by introducing a flexible hierarchical Bayesian transmission model and collecting the largest dataset of NPI implementation dates across Europe. Business closures, educational institution closures, and gathering bans reduced transmission, but reduced it less than they did in the first wave. This difference is likely due to organisational safety measures and individual protective behaviours—such as distancing—which made various areas of public life safer and thereby reduced the effect of closing them. Specifically, we find smaller effects for closing educational institutions, suggesting that stringent safety measures made schools safer compared to the first wave. Second-wave estimates outperform previous estimates at predicting transmission in Europe’s third wave.

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