Analytic expressions for the BCDMEM model of recognition memory

We introduce a Fourier transformation technique that enables one to derive closed-form expressions of performance measures (e.g., hit and false alarm rates) of simulation-based models of recognition memory. Application of the technique is demonstrated using the bind cue decide model of episodic memory (BCDMEM; [Dennis, S., & Humphreys, M.S. (2001). A context noise model of episodic word recognition. Psychological Review, 108(2), 452-478]). In addition to reducing the time required to test the model, which for models like BCDMEM can be excessive, asymptotic expressions of the measures reveal heretofore unknown properties of the model, such as model predictions being dependent on vector length.