Threshold training of two-mode signal detection

In certain systems of signal detection and pattern recognition, the process of training an observer to distinguish levels of sensory excitation or to recognize patterns, involves an adaptive threshold adjustment. These "threshold learning processes" (TLPs) can be modeled by finite-state Markov chains. When the output statistics of these TLPs move at random between two sets of parameters, we have a "two-mode" TLP. A probabilistic measure of the training and working performance of two-mode TLPs is proposed. A method of designing periodic train-work schedules for two-mode TLPs is described. For many two-mode TLPs the ratio of working time to retraining time yielding a desired performance level is maximized when the work-retrain period is made as small as possible. The final success probability in a working phase of any two-mode Markov chain cannot be less than one-half of the success probability at the beginning of that working phase. Train-work schedules can exploit the adaptive properties of trainable detectors to overcome not only the unpredictability of the mode, but also the designer's ignorance of the channel statistics.