Abstract
Integration-to-bound models are among the most widely used models of perceptual decision-making due to their simplicity and power in accounting for behavioral and neurophysiological data. They involve temporal integration over an input signal (“evidence”) plus Gaussian white noise. However, brain data shows that noise in the brain is long-term correlated, with a spectral density of the form 1/fα (with typically 1 < α < 2), also known as pink noise or ‘1/f’ noise. Surprisingly, the adequacy of the spectral properties of drift-diffusion models to electrophysiological data has received little attention in the literature. Here we propose a model of accumulation of evidence for decision-making that takes into consideration the spectral properties of brain signals. We develop a generalization of the leaky stochastic accumulator model using a Langevin equation whose non-linear noise term allows for varying levels of autocorrelation in the time course of the decision variable. We derive this equation directly from magnetoencephalographic data recorded while subjects performed a spontaneous movement-initiation task. We then propose a nonlinear model of accumulation of evidence that accounts for the ‘1/f’ spectral properties of brain signals, and the observed variability in the power spectral properties of brain signals. Furthermore, our model outperforms the standard drift-diffusion model at approximating the empirical waiting time distribution.
Highlights
Neurophysiological recordings and behavioral data support the view that decision-making in humans is intrinsically a noisy process
We develop a generalization of the leaky stochastic accumulator model using a Langevin equation whose non-linear stochastic term allows for trajectories with varying levels of temporal autocorrelation, referred as ‘nonlinear model’, because it is nonlinear both in the deterministic and the stochastic part of the corresponding Langevin equation
We have derived stochastic differential equations that describe the neural dynamics of human subjects, as recorded by magnetoencephalography (MEG) during a self-initiated movement task[7]
Summary
Neurophysiological recordings and behavioral data support the view that decision-making in humans is intrinsically a noisy process. We consider a more general version of the DDM currently used in the literature, by adding leakage to the drift term This model is usually referred as a “leaky stochastic accumulator model”[7] (LSA, known as the Ornstein-Uhlenbeck process[11]). This is an important fact, that points towards the possible presence of nonlinearities in the Langevin coefficients both in abnormal brain dynamics and in normal subjects, and emphasizes the general importance of the specific nonlinear dependencies of Langevin coefficients for discriminating physiological states If these nonlinearities were present during the accumulation of evidence, an important revision of current accumulator models might be called for, especially in contexts where the drift term is quite small relative to the noise, as in the case of spontaneous self-initiated movement[7,9,17]
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