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A probabilistic, distributed, recursive mechanism for decision-making in the brain

Fig 9

The mean number of ISIs to decision in continuous-time spike-trains is equivalent to the mean number observations to decision in discrete time.

C sensory neurons (input channels; left) produce sequences of ISIs in continuous time with mean μ*n (red; best tuned to the stimulus) or μ0n (black; otherwise). The average decision time—between decision initiation (Init) and termination (Term)—is τc in correct trials, as in this diagram. In discrete time it takes an average of 〈Tc vector observations, x(t) (composed of scalar observations xi(t), each time step t; blue), to make decisions. [20] showed that in the minimum input case (when C = N), the mean number of ISIs in the most active channel (red) used by a general, continuous-time, spike-based instance of the MSPRT, approximately equal the mean number of observations, 〈Tc, required by the simpler, discrete-time MSPRT (here 7 in both cases), which carries to our identically-performing rMSPRT; this is true under equal input channel statistics (μ*, μ0, σ*, σ0), data distributions (e.g. all lognormal), number of alternatives, N, and error rate, ϵ. This all implies that, if we add 0.5—the expected number of ISIs from decision initiation to a first spike—to 〈Tc, and multiply this by the minimum mean ISI, μ*n (of fastest firing channel), this approximately equals τc, hence Eq 14; conversely, in error trials we use μ0 and 〈Te, to get τe (Eq 15).

Fig 9

doi: https://doi.org/10.1371/journal.pcbi.1006033.g009