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

Area of Science:

• Cognitive Science
• Computational Neuroscience
• Mathematical Psychology

Background:

• Decision-making is frequently modeled using first-passage time problems for stochastic differential equations, particularly drift-diffusion processes.
• These models, with constant or time-varying drift rates and noise, effectively reproduce behavioral data like accuracy and response times, and neuronal firing rates.
• Exact solutions for first-passage problems with time-varying drift rates remain elusive.

Purpose of the Study:

• To develop and evaluate approximate methods for obtaining closed-form expressions for response time distributions in time-varying drift-diffusion models.
• To assess the utility of an interrogation or cued-response protocol for approximating first-passage time distributions in evidence accumulation models.
• To compare the performance of these approximations against exact solutions for constant drift cases and empirical data from sigmoidal functions.

Main Methods:

• Utilized an interrogation or cued-response protocol to derive approximate first-passage time distributions for a specific class of time-varying drift-diffusion processes.
• Compared the derived approximate distributions with exact solutions available for constant drift scenarios.
• Evaluated the approximations against empirical data characterized by sigmoidal functions.

Main Results:

• Both direct interrogation and error-minimizing interrogation approximations can successfully capture diverse response time distribution shapes and mode numbers.
• The direct interrogation approximation demonstrates a systematic bias when compared to the exact free response distribution.
• The developed approximations offer a viable approach for modeling evidence accumulation with time-varying parameters where exact solutions are unavailable.

Conclusions:

• Interrogation protocols provide valuable approximate solutions for response time distributions in time-varying drift-diffusion models, crucial for modeling and inference.
• While effective in capturing distribution characteristics, the direct approximation method requires careful consideration due to systematic biases.
• These findings advance the ability to model complex decision-making processes with dynamic evidence accumulation.