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A Bayesian Attractor Model for Perceptual Decision Making
Fig 3
Illustration of the inference scheme used for decision making in the BAttM.
In the physical environment a stimulus is presented by the experimenter and observed by the subject. Components inside the shaded rectangle model internal processes of the subject. Sensory processes in the subject’s brain translate the stimulus into an abstract feature representation xt. The input model (i, green) of the BAttM approximates this translation by mapping the stimulus identity (decision alternative At at time t) to a value xt drawn from a Gaussian distribution with mean μt and covariance s2 I. The generative model (ii, orange) states that the decision state z is represented by a Gaussian 
and evolves according to Hopfield dynamics (Eq 2). The generative model further maps the decision state to different Gaussian densities over observations which mirror those in the input process (Eq 3). Consequently, for the next time step, the generative model predicts the distribution of the decision state, 
, and the distribution of the observation, 
, which critically depend on model parameters q and r, respectively. The cross-covariance between predicted decision state and predicted observation is denominated 
. Bayesian inference (iii, red) iteratively compares observations xt with predictions 
and updates the estimate of the decision state (Eq 4) via the Kalman gain Kt which processes the uncertainty defined by 
and 
(Eq 5). The decision criterion (iv, blue) is defined as a bound λ on an explicit measure of confidence (Eq 6).
doi: https://doi.org/10.1371/journal.pcbi.1004442.g003