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Closed-form approximations of first-passage distributions for a stochastic decision making model

Biomedical Sciences Research Institute Computer Science Research Institute Environmental Sciences Research Institute Nanotechnology & Advanced Materials Research Institute

Broderick, Tamara, Wong-Lin, KongFatt and Holmes, Philip (2010) Closed-form approximations of first-passage distributions for a stochastic decision making model. Applied Mathematics Research eXpress, 2009 (2). pp. 123-141. [Journal article]

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URL: http://amrx.oxfordjournals.org/content/2009/2/123.abstract

DOI: 10.1093/amrx/abp008

Abstract

In free response choice tasks, decision making is often modeled as a first-passage problemfor a stochastic differential equation. In particular, drift-diffusion processes withconstant or time-varying drift rates and noise can reproduce behavioral data (accuracyand response-time distributions) and neuronal firing rates. However, no exact solutionsare known for the first-passage problem with time-varying data. Recognizing the importanceof simple closed-form expressions for modeling and inference, we show that an interrogationor cued-response protocol, appropriately interpreted, can yield approximatefirst-passage (response time) distributions for a specific class of time-varying processesused to model evidence accumulation. We test these against exact expressions for theconstant drift case and compare them with data from a class of sigmoidal functions. Wefind that both the direct interrogation approximation and an error-minimizing interrogationapproximation can capture a variety of distribution shapes and mode numbersbut that the direct approximation, in particular, is systematically biased away from thecorrect free response distribution.

Item Type:Journal article
Faculties and Schools:Faculty of Computing & Engineering
Faculty of Computing & Engineering > School of Computing and Intelligent Systems
Research Institutes and Groups:Computer Science Research Institute
Computer Science Research Institute > Intelligent Systems Research Centre
ID Code:21346
Deposited By:Dr Kongfatt Wong-Lin
Deposited On:09 Mar 2012 15:03
Last Modified:09 Mar 2012 15:03

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