Signal Detection Theory (SDT) explains how a receiver detects a signal in noise as a function of the receiver's sensitivity to the signal & the receiver's bias or tendency to assert the presence of the signal whether it is there or not.
Signal Detection Theory (SDT) explains how a receiver detects a signal in noise as a function of the receiver's sensitivity to the signal & the receiver's bias or tendency to assert the presence of the signal whether it is there or not.
Given that a signal may be present or not, and the receiver may assert that the signal is present or not, there are four possibilities:
Signal:
Present Not present
Receiver: ---------------------------
| | |
'Present' | Hit | False alarm |
| | |
---------------------------
| | |
'Not present' | Miss | Correct |
| | rejection |
---------------------------
The number of Hits divided by (Hits + Misses) is the hit rate ($h$), and the number of False alarms divided by (False alarms + Correct rejections) is the false alarm rate ($fa$). These can be decomposed into the sensitivity ($d'$) and bias ($c$) of the receiver:
\begin{align}
d' &= \Phi^{-1}(h) - \Phi^{-1}(fa) \\\
\ \\\
c &= \frac{\Phi^{-1}(h) + \Phi^{-1}(fa)}{2}
\end{align}
Note that the "four possibilities" above constitutes a confusion matrix, and that the hit and false alarm rate are related to many standard metrics for confusion matrices. Specifically, the hit rate is the same as sensitivity, and the false alarm rate is the same as $1-$specificity.
