Work

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

Year: 2010

Type: article

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.

Source: Applied Mathematics Research eXpress

DOI: 10.1093/amrx/abp008

Authors: T. Broderick, K. F. Wong-Lin, P. Holmes

Institution: University of California, Berkeley

Language: English

Topic: Decision-Making and Behavioral Economics

Subfield: General Decision Sciences

Field: Decision Sciences

Domain: Social Sciences

Open Access status: bronze

Funder: National Institute of Mental Health

Award: Cognitive and Neural Mechanisms of Decision and Control