Extreme-value signal detection theory for recognition memory: The parametric road not taken

Area of Science:

• Cognitive Psychology
• Psychophysics
• Mathematical Psychology

Background:

• Signal detection theory (SDT) is a standard framework in psychological research, especially for recognition memory.
• The conventional Gaussian assumption in SDT has limitations and is based on convenience rather than necessity.

Purpose of the Study:

• To critically examine the limitations of the Gaussian assumption in SDT.
• To propose and validate an alternative parametric model for recognition memory based on extreme-value distributions.
• To introduce and evaluate the Gumbel_min model as a principled alternative.

Main Methods:

• Developed a signal detection theory model using extreme-value distributions (event minima).
• Empirically validated the invariance principle under uniform choice-set expansions in a recognition memory experiment.
• Benchmarked the Gumbel_min model against the Gaussian model across various recognition memory tasks.

Main Results:

• The proposed extreme-value distribution model, specifically the Gumbel_min model, offers a principled parametric alternative to the Gaussian assumption.
• Empirical validation confirmed the behavioral principle of invariance under uniform choice-set expansions.
• The Gumbel_min model successfully characterized recognition memory judgments across diverse experimental paradigms.

Conclusions:

• The Gumbel_min model provides a parsimonious and effective characterization of recognition memory.
• The model's discriminability index, g', is directly computable from hit and false-alarm rates, offering practical utility.