Fig. 2: The POMDP model of the direction discrimination task.
a Our modeling framework depicting the real world generative model and the decision maker’s model. In each trial, the state (here signed coherence c) is generated from a prior (here a discrete set selected by the experimenter). Given a value for c for a trial, all of the observations zi in that trial are independent samples generated from an observation function (\({{{{{{{\mathcal{N}}}}}}}}(\mu =c,{w}_{z})\)). While the decision maker has full access to the observations, the prior distribution and the observation function are not known. Our POMDP model estimates these two distributions as \({{{{{{{\mathcal{N}}}}}}}}({\mu }_{0}=0,{\sigma }_{0})\) and \({{{{{{{\mathcal{N}}}}}}}}({c}_{z},{\sigma }_{z})\) where σ0 and σz are learned from data (see text), and cz is the coherence which is estimated by the subject using the belief \({{{{{{{\mathcal{N}}}}}}}}({\mu }_{t},{\sigma }_{t})\) as described in the text. b Probability distribution of momentary observations for a motion coherence c is modeled as a Gaussian distribution with mean μ = c and variance \({w}_{z}^{2}\). There are multiple Gaussian distributions for different motion coherences. Positive and negative observations indicate rightward and leftward motion directions, respectively. c The distribution of inferred coherence across all trials provides the initial belief state of the POMDP model (blue histogram) at the beginning of each trial. The initial belief is approximated by a Gaussian function (red curve). d The POMDP model sequentially updates its belief about the motion coherence based on new observations. Combining the belief at time t − 1 (green distribution) with the acquired observation from the stimulus at time t (blue distribution) results in a new belief at t (red distribution). The expected likelihood that the rightward choice is correct is the area under the updated belief distribution for positive sensory evidence (yellow region).
