Decision-time statistics of nonlinear diffusion models: Characterizing long sequences of subsequent trials

Author(s)

Vellmer, Sebastian ^[1] ; Lindner, Benjamin

Affiliation

^[1] Humboldt Univ, Phys Dept, D-12489 Berlin - Germany

• Document type: Journal article
• Source: JOURNAL OF MATHEMATICAL PSYCHOLOGY; v. 99, DEC 2020.
• Web of Science Citations: 0

Abstract

Cognitive models of decision making are an important tool in studies of cognitive psychology and have been successfully used to fit experimental data and to relate them to neurophysiological mechanisms in the brain. One of the most important models for binary decision making is the diffusion-decision model (DDM) in which a diffusion process that models the accumulation of perceived evidence yields the decisions upon reaching one of two thresholds. Due to its simplicity, the model is analytically tractable and has been used to bridge the gap between implementations of decision making in neurobiologically plausible neural networks and experiments. However, biologically realistic network models exhibit nonlinear dynamics that yield via mean-field-reduction techniques a nonlinear DDM for which analytical solutions and proper numerical tools in general are not known. Furthermore, although often agents have to make a number of subsequent decisions, the statistics of such sequences of decisions (containing information on whether the decisions are correct or incorrect and on their timing) are so far poorly understood. Here we introduce the decision trains, sequences of negative or positive spikes at the decision times with the sign corresponding to the correctness of the decision. The decision trains enable a proper characterization of experiments in which many trials are performed consecutively. For the principal reference case of independent decisions (renewal statistics), we derive relations between the second-order statistics of the decision trains (i.e. their power spectra) and the response-time densities. Most importantly, we extend an efficient numerical procedure for spiking neuron models, the threshold-integration method, to determine the temporal statistics of nonlinear DDMs. The threshold-integration method provides the temporal statistics, i.e. decision rates, decision-time densities and the decision-train power spectra. Moreover, the procedure is used for the calculation of the linear response to a sinusoidal modulation. We compare all results with direct simulations of the stochastic model. (C) 2020 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 15/50122-0 - Dynamic phenomena in complex networks: basics and applications
• Grantee: Elbert Einstein Nehrer Macau
• Support Opportunities: Research Projects - Thematic Grants