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PLoS Comput Biol. 2015 Oct 30;11(10):e1004519. doi: 10.1371/journal.pcbi.1004519. eCollection 2015 Oct.

Doubly Bayesian Analysis of Confidence in Perceptual Decision-Making.

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Gatsby Computational Neuroscience Unit, University College London, London, United Kingdom.
Department of Experimental Psychology, University of Oxford, Oxford, United Kingdom; Calleva Research Centre for Evolution and Human Sciences, Magdalen College, University of Oxford, Oxford, United Kingdom; Interacting Minds Centre, Aarhus University, Aarhus, Denmark.
Interacting Minds Centre, Aarhus University, Aarhus, Denmark; Institute of Cognitive Neuroscience, University College London, London, United Kingdom.


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.

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