An integration-to-bound model of decision-making that accounts for the spectral properties of neural data

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/f^α (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.