Asy, initial choices and switches are speedy (thick lines). The position of your fixed point, to which the dynamics converges, depends strongly on I. (B, C): In the Bayesian attractor model timing and accuracy of initial choices and re-decisions depend on the uncertainties in the model, PubMed ID:http://www.ncbi.nlm.nih.gov/pubmed/20181482 but, critically, the place of your fixed points from the dynamics stay the exact same for different uncertainties. B and C share the same observations with noise level s = 1. In B: q = 0.five. In C: r = 1.9. doi:10.1371/journal.pcbi.1004442.gr and q such that anticipated stimulus strength is automatically taken into account in the course of evidence computation from the stimulus. As a consequence of stable fixed point areas, a deviation in the selection state from a fixed point could be readily interpreted as violation with the expectations concerning the stimulus linked with that fixed point, irrespective of stimulus strength. Normally, the extra such expectations are violated, the less confident the selection maker needs to be about choosing among the alternatives. We implemented this mechanism in the BattM by deriving the self-confidence within a decision alternative directly from the probabilistic model and applying a threshold on it as selection criterion (see Models, Eq 6). In Fig 10 we illustrate how confidence values relate to the posterior density on the selection state (Fig 10A), and how confidence-based decisions are made (Fig 10B). Intuitively, the confidence for a precise alternative measures the distance with the existing decision state (blue and orange lines in Fig 10A) from the steady fixed point of that option (at [0, 10] or [10, 0]) scaled by the posterior uncertainty from the selection state. Consequently, the confidence for all options could be tracked across time (cf. blue and orange lines in Fig 10B). Strikingly, the self-assurance dynamics are diverse from the decision variable dynamics: Though the decisionPLOS Computational Biology | DOI:10.1371/journal.pcbi.1004442 August 12,18 /A Bayesian Attractor Model for Perceptual Decision MakingFig ten. Example evolution in the posterior density of the decision state plus the linked self-confidence values for a single trial using a switch of stimulus at 800ms (vertical, get BGP-15 dotted line). (A) Posterior density from the selection state with mean (coloured lines) and two instances standard deviation (shading) of decision state variables as in Fig 8A. Grey, dashed lines in a show the decision instances for the initial decision (92ms) and also the re-decision soon after the switch (1160ms). (B) Solid lines indicate self-confidence values for each options, i.e., the posterior probability density values that the selection state is in one of the stable fixed points on the attractor dynamics. The choice threshold is indicated as grey, dashed line. The parameters with the model were these of Fig 7B (r = 2.four, s = 4, q = 0.5). doi:ten.1371/journal.pcbi.1004442.gstate gradually moves towards a fixed point, as a result reflecting the comparatively slow gradual accumulation of evidence (e.g., time period 800 to 1100ms), the confidence rises abruptly as soon as the posterior density of the selection state starts concentrating about a fixed point (e.g., from 1100ms onwards). How does the confidence-based decision generating formalism compare with experimental findings Early behavioural function with humans [42], indirect self-confidence judgements by rats [41] and general theoretical considerations [42, 43] recommend that confidence in appropriate selections increases with stimulus strength whereas confide.
