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WOLFRAM NOTEBOOK
Signal Detection Theory
Signal Detection Theory
Signal detection theory is a principled explanation for decision making under noisy conditions. All real decisions are made under a certain degree of uncertainty determined by extrinsic environmental conditions and intrinsic neural and cognitive processes.
A typical situation of concern to the theory is the simple forced choice, a type of binary classifier system. In this situation, a subject must decide whether some type of signal (perhaps a flashing light) is present in trials that contain the signal and trials that do not contain the signal. If during a signal trial the subject decides a signal is present, the decision is called a hit; if the subject decides a signal is not present, the decision is called a miss. If during a non-signal trial the subject decides a signal is not present, the decision is called a correct rejection; if the subject decides a signal is present, the decision is called a false alarm. A variable called the internal response is what "causes" the subject to make a certain decision, and is often related to a neuronal parameter such as firing rate.
The internal responses for signal and non-signal trials are described by Gaussian probability distributions; in this Demonstration, the red distribution is for the non-signal situation and the green distribution is for the signal situation. Discriminability is a measure of the extent to which a subject can distinguish between a signal situation and a non-signal situation and is quantified by the distance between the means of both distributions. The criterion is a variable usually set by the subject; it is a strategy for decision making in which an internal response above the criterion "causes" a "yes, signal" response and an internal response below the criterion "causes" a "no, no signal" response. Also shown in this Demonstration is a receiver operating characteristic (ROC) curve, which shows how the hit rate and false alarm rate vary with discriminability and noise.