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  3. Efficient Inference In First Passage Time Models.
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Efficient Inference in First Passage Time Models.

Sicheng Liu1, Alexander Fengler2, Michael J Frank2,3

  • 1Division of Applied Mathematics, Brown University, 182 George St, Providence, 02912, RI, USA.

Statistics and Computing
|March 30, 2026

View abstract on PubMed

Summary
This summary is machine-generated.

We developed a faster algorithm for generalized drift diffusion models (GDDMs) used in cognitive neuroscience. This method accurately computes likelihood functions, improving statistical inference for decision-making models with dynamic parameters.

Keywords:
Cherkasov conditionattentiondrift diffusion modelfirst passage timelikelihood-based inferencenumerical methods

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Area of Science:

  • Computational cognitive neuroscience
  • Mathematical modeling
  • Statistical inference

Background:

  • First passage time models are crucial for analyzing random processes across scientific disciplines.
  • Generalized drift diffusion models (GDDMs) are vital in cognitive neuroscience for understanding decision-making by modeling latent psychological processes.
  • Current methods for computing GDDM likelihoods are inefficient when drift rates vary dynamically within trials.

Purpose of the Study:

  • To propose a novel, fast, and flexible algorithm for computing the likelihood function of GDDMs.
  • To address limitations of existing methods in scenarios with time-varying drift rates.
  • To enable more efficient statistical inference for complex GDDMs.

Main Methods:

  • Developed a new algorithm for GDDMs satisfying the Cherkasov condition.
  • The method segments trials into discrete stages.
  • Fast analytical results are used for stage-wise densities, which are then integrated for trial-wise likelihood computation.

    • Main Results:

    • The proposed algorithm provides accurate likelihood evaluations for statistical inference.
    • The method significantly outperforms existing approaches in terms of computational speed.
    • Demonstrated effectiveness through numerical examples for GDDMs with dynamic drift rates.

    Conclusions:

    • The new algorithm offers a substantial improvement for analyzing GDDMs, particularly in complex scenarios.
    • This advancement facilitates more efficient and accurate parameter estimation in computational cognitive neuroscience.
    • The method enhances the applicability of GDDMs to real-world data with dynamic covariates.