Time-dependent Poisson counter models of response latency in simple judgment

Area of Science:

• Cognitive psychology
• Computational neuroscience
• Mathematical modeling

Background:

• Sequential-sampling models are crucial for understanding response time (RT).
• The Poisson counter model assumes exponentially distributed waiting times between evidence increments.
• Existing models often lack flexibility in modeling dynamic evidence accumulation.

Purpose of the Study:

• To generalize the Poisson counter model by incorporating time-varying Poisson event rates.
• To derive general expressions for response time distributions in multi-alternative scenarios.
• To provide closed-form solutions for response probabilities and mean RT under specific rate assumptions.

Main Methods:

• Developed a generalized Poisson counter model with time-dependent event rates.
• Derived mathematical expressions for response time distributions for two- and m-alternative choices.
• Obtained closed-form solutions for response probabilities and mean RT under proportional and power-law integrated rates.

Main Results:

• General expressions for RT distributions were derived for the first time with time-varying rates.
• Closed-form solutions were found for response probabilities and mean RT under specific conditions.
• The model was applied to early vision, linking Poisson rates to sustained and transient channel outputs.

Conclusions:

• The generalized Poisson counter model provides a more flexible framework for analyzing RT data.
• This model advances the understanding of decision-making under dynamic evidence accumulation.
• The application in early vision highlights the model's utility in explaining neural processes.