= 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,,0,,'' leads to the use of the magnitude of ''x'' as a criterion (''e.g.'' Choose ''H,,1,,'' when ''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,,0,,)''). These two quantities are also known in '''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 [[Glossary#ROC| ROC or Receiver Operating Charactistic]].