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

Tamara Broderick, KongFatt Wong-Lin, Philip Holmes

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    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.
    LanguageEnglish
    Pages123-141
    JournalApplied Mathematics Research eXpress
    Volume2009
    Issue number2
    DOIs
    Publication statusPublished - 11 Feb 2010

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    Differential equations
    Decision making

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    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 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.",
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    Closed-form approximations of first-passage distributions for a stochastic decision making model. / Broderick, Tamara; Wong-Lin, KongFatt; Holmes, Philip.

    In: Applied Mathematics Research eXpress, Vol. 2009, No. 2, 11.02.2010, p. 123-141.

    Research output: Contribution to journalArticle

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    AU - Holmes, Philip

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    AB - 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.

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