Stochastic Dynamic Models of Response Time and Accuracy: A Foundational Primer

Area of Science:

• Cognitive Science
• Mathematical Psychology
• Computational Neuroscience

Background:

• Many statistical decision models for information processing use linear, first-order stochastic differential equations (SDEs).
• The first passage time of diffusion processes through response criteria determines decision times in these models.
• Time-inhomogeneous SDEs, arising from common cognitive model assumptions, render classical solution methods inapplicable.

Purpose of the Study:

• To describe recent integral equation methods for solving first passage time problems in cognitive models.
• To demonstrate the applicability of these methods to both one-sided and two-sided problems.
• To provide illustrative applications relevant to cognitive modelers.

Main Methods:

• Utilizing integral equation methods to solve first passage time problems for diffusion processes.
• Addressing time-inhomogeneous stochastic differential equations (SDEs).
• Applying methods to both one-sided and two-sided first passage time scenarios.

Main Results:

• Integral equation methods provide solutions for first passage time problems even with time-inhomogeneous SDEs.
• These methods are effective for both one-sided and two-sided first passage time calculations.
• The described techniques are particularly relevant for developing and analyzing cognitive models.

Conclusions:

• Integral equation methods offer a powerful alternative to classical approaches for solving first passage time problems in cognitive modeling.
• These methods successfully handle the complexities of time-inhomogeneous SDEs.
• The detailed description and applications facilitate their use by researchers in cognitive science and related fields.