Journal Article

Closed-Form Approximations of First-Passage Distributions for a Stochastic Decision-Making Model

Tamara Broderick, Kong Fatt Wong-Lin and Philip Holmes

in Applied Mathematics Research eXpress

Volume 2009, issue 2, pages 123-141
Published in print January 2009 | ISSN: 1687-1200
Published online February 2010 | e-ISSN: 1687-1197 | DOI: https://dx.doi.org/10.1093/amrx/abp008

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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.

Journal Article.  5467 words.  Illustrated.

Subjects: Applied Mathematics