Time-Varying Perturbations Can Distinguish Among Integrate-to-Threshold Models for Perceptual Decision Making in Reaction Time Tasks

Several integrate-to-threshold models with differing temporal integration mechanisms have been proposed to describe the accumulation of sensory evidence to a prescribed level prior to motor response in perceptual decision-making tasks. An experiment and simulation studies have shown that the introduction of time-varying perturbations during integration may distinguish among some of these models. Here, we present computer simulations and mathematical proofs that provide more rigorous comparisons among one-dimensional stochastic differential equation models. Using two perturbation protocols and focusing on the resulting changes in the means and standard deviations of decision times, we show that for high signal-to-noise ratios, drift-diffusion models with constant and time-varying drift rates can be distinguished from Ornstein-Uhlenbeck processes, but not necessarily from each other. The protocols can also distinguish stable from unstable Ornstein-Uhlenbeck processes, and we show that a nonlinear integrator can be distinguished from these linear models by changes in standard deviations. The protocols can be implemented in behavioral experiments.

[1]  J. Gold,et al.  The neural basis of decision making. , 2007, Annual review of neuroscience.

[2]  R. Mazo.  On the theory of brownian motion , 1973 .

[3]  KongFatt Wong-Lin,et al.  Neural Circuit Dynamics Underlying Accumulation of Time-Varying Evidence During Perceptual Decision Making , 2007, Frontiers Comput. Neurosci..

[4]  Eric T. Shea-Brown,et al.  A firing rate model of Parkinsonian deficits in interval timing , 2006, Brain Research.

[5]  P. Holmes,et al.  MODELING A SIMPLE CHOICE TASK: STOCHASTIC DYNAMICS OF MUTUALLY INHIBITORY NEURAL GROUPS , 2001 .

[6]  Anders Ledberg,et al.  Neurobiological Models of Two-Choice Decision Making Can Be Reduced to a One-Dimensional Nonlinear Diffusion Equation , 2008, PLoS Comput. Biol..

[7]  J. Schall.  Neural correlates of decision processes: neural and mental chronometry , 2003, Current Opinion in Neurobiology.

[8]  Xiao-Jing Wang,et al.  Cortico–basal ganglia circuit mechanism for a decision threshold in reaction time tasks , 2006, Nature Neuroscience.

[9]  Philip Holmes,et al.  Rapid decision threshold modulation by reward rate in a neural network , 2006, Neural Networks.

[10]  Rafal Bogacz,et al.  Bounded Ornstein–Uhlenbeck models for two-choice time controlled tasks , 2010 .

[11]  Xiao-Jing Wang,et al.  A Recurrent Network Mechanism of Time Integration in Perceptual Decisions , 2006, The Journal of Neuroscience.

[12]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1951 .

[13]  J. Cowan,et al.  A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue , 1973, Kybernetik.

[14]  R. Duncan Luce,et al.  Response Times: Their Role in Inferring Elementary Mental Organization , 1986 .

[15]  Roger Ratcliff,et al.  A Theory of Memory Retrieval. , 1978 .

[16]  Philip L. Smith,et al.  Psychology and neurobiology of simple decisions , 2004, Trends in Neurosciences.

[17]  Philip Holmes,et al.  Simple Neural Networks that Optimize Decisions , 2005, Int. J. Bifurc. Chaos.

[18]  M. Shadlen,et al.  Decision-making with multiple alternatives , 2008, Nature Neuroscience.

[19]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[20]  W. Newsome,et al.  What electrical microstimulation has revealed about the neural basis of cognition , 2004, Current Opinion in Neurobiology.

[21]  Timothy D. Hanks,et al.  Microstimulation of macaque area LIP affects decision-making in a motion discrimination task , 2006, Nature Neuroscience.

[22]  M. Shadlen,et al.  A role for neural integrators in perceptual decision making. , 2003, Cerebral cortex.

[23]  G. Uhlenbeck,et al.  On the Theory of the Brownian Motion II , 1945 .

[24]  Albert Compte,et al.  Neural Integrator Models , 2009 .

[25]  Alexander C. Huk,et al.  Temporal Dynamics Underlying Perceptual Decision Making: Insights from the Interplay between an Attractor Model and Parietal Neurophysiology , 2008, Front. Neurosci..

[26]  P. Mazur.  On the theory of brownian motion , 1959 .

[27]  J. Ditterich.  Evidence for time‐variant decision making , 2006, The European journal of neuroscience.

[28]  Xiao-Jing Wang,et al.  Probabilistic Decision Making by Slow Reverberation in Cortical Circuits , 2002, Neuron.

[29]  M. Shadlen,et al.  Microstimulation of visual cortex affects the speed of perceptual decisions , 2003, Nature Neuroscience.

[30]  B. Lindner.  Moments of the First Passage Time Under External Driving , 2003, cond-mat/0312017.

[31]  J. Schall,et al.  Neural Control of Voluntary Movement Initiation , 1996, Science.

[32]  James L. McClelland,et al.  The time course of perceptual choice: the leaky, competing accumulator model. , 2001, Psychological review.

[33]  Roger Ratcliff,et al.  The Diffusion Decision Model: Theory and Data for Two-Choice Decision Tasks , 2008, Neural Computation.

[34]  R. Ratcliff.  Modeling response signal and response time data , 2006, Cognitive Psychology.

[35]  G. Uhlenbeck,et al.  On the Theory of the Brownian Motion , 1930 .

[36]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.

[37]  Jonathan D. Cohen,et al.  The physics of optimal decision making: a formal analysis of models of performance in two-alternative forced-choice tasks. , 2006, Psychological review.

[38]  M. Shadlen,et al.  Neural Activity in Macaque Parietal Cortex Reflects Temporal Integration of Visual Motion Signals during Perceptual Decision Making , 2005, The Journal of Neuroscience.

[39]  Philip Holmes,et al.  A Neural Network Model of the Eriksen Task: Reduction, Analysis, and Data Fitting , 2008, Neural Computation.

[40]  Jochen Ditterich,et al.  Stochastic models of decisions about motion direction: Behavior and physiology , 2006, Neural Networks.

[41]  R. Ratcliff,et al.  Connectionist and diffusion models of reaction time. , 1999, Psychological review.

[42]  Desmond J. Higham,et al.  An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations , 2001, SIAM Rev..

[43]  Philip L. Smith,et al.  Attention orienting and the time course of perceptual decisions: response time distributions with masked and unmasked displays , 2004, Vision Research.

[44]  M. Posner.  Chronometric explorations of mind , 1978 .

[45]  M. Shadlen,et al.  Response of Neurons in the Lateral Intraparietal Area during a Combined Visual Discrimination Reaction Time Task , 2002, The Journal of Neuroscience.