# Signal Detection Theory

At its simplest, SignalDetectionTheory or SDT is a model for the situation of a decision maker choosing between two hypotheses based on the value of a measurement, *x*.

Under H_{1}, *x* comes from the **Signal** distribution *f _{1}* and under H

_{0},

*x*comes from the

**Noise**distribution

*f*.

_{0}It is the job of the **Observer** to decide whether it was 'Signal' or 'Noise' that produced *x*.

The assumption that larger values of *x* are more typical under *f _{1}* than under

*f*leads to the use of the magnitude of

_{0}*x*as a criterion (

*e.g.*Choose

*H*when

_{1}*x>c*, otherwise chose

*H*).

_{0}The performance of this criterion is given by the Hit Rate (*P(x>c|f _{1})*) and the False Alarm Rate (

*P(x>c|f*). These two quantities are also known in

_{0})**Neyman-Pearson-land**as

**Power**&

**Size**, or as

**Sensitivity**and

**1-Specificity**(the complement of

**Specificity**).

When *1-Specificity* is plotted against *Sensitivity* as a function of the criterion *c* the resulting curve is known as the ROC or Receiver Operating Charactistic.