Time-varying perturbations can distinguish among integrate-to-threshold models for perceptual decision-making in reaction time tasks

TL;DR

This study uses simulations and mathematical proofs to show how time-varying perturbations can differentiate among various integrate-to-threshold models in perceptual decision-making, especially under high signal-to-noise ratios.

Contribution

The paper provides rigorous comparisons and protocols to distinguish different stochastic differential equation models of decision-making using perturbations and statistical measures.

Findings

High signal-to-noise ratios allow distinguishing drift-diffusion from Ornstein-Uhlenbeck models.

Protocols can differentiate stable from unstable Ornstein-Uhlenbeck processes.

Nonlinear integrators can be distinguished by changes in decision time variability.

Abstract

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.