title: Closed-Form Approximations of First-Passage Distributions for a Stochastic Decision-Making Model.
abstract: In free response choice tasks, decision making is often modeled as a first-passage problem for a stochastic differential equation. In particular, drift-diffusion processes with constant or time-varying drift rates and noise can reproduce behavioral data (accuracy and response-time distributions) and neuronal firing rates. However, no exact solutions are known for the first-passage problem with time-varying data. Recognizing the importance of simple closed-form expressions for modeling and inference, we show that an interrogation or cued-response protocol, appropriately interpreted, can yield approximate first-passage (response time) distributions for a specific class of time-varying processes used to model evidence accumulation. We test these against exact expressions for the constant drift case and compare them with data from a class of sigmoidal functions. We find that both the direct interrogation approximation and an error-minimizing interrogation approximation can capture a variety of distribution shapes and mode numbers but that the direct approximation, in particular, is systematically biased away from the correct free response distribution.
authors.affiliation: Department of Statistics, University of California, Berkeley, CA 94720, USA.
authors.forename: Tamara
authors.initials: T
authors.lastname: Broderick
authors.forename: Kong Fatt
authors.initials: KF
authors.lastname: Wong-Lin
authors.forename: Philip
authors.initials: P
authors.lastname: Holmes