Detection theory or signal detection theory is a means to measure the ability to differentiate between information-bearing patterns (called stimulus in living organisms, signal in machines) and random patterns that distract from the information (called noise, consisting of background stimuli and random activity of the detection machine and of the nervous system of the operator).
In the field of electronics, signal recovery is the separation of such patterns from a disguising background.
The theory can explain how changing the threshold will affect the ability to discern, often exposing how adapted the system is to the task, purpose or goal at which it is aimed.
When the detecting system is a human being, characteristics such as experience, expectations, physiological state (e.g. fatigue) and other factors can affect the threshold applied.
For instance, a sentry in wartime might be likely to detect fainter stimuli than the same sentry in peacetime due to a lower criterion, however they might also be more likely to treat innocuous stimuli as a threat.
[2] By 1954, the theory was fully developed on the theoretical side as described by Peterson, Birdsall and Fox[3] and the foundation for the psychological theory was made by Wilson P. Tanner, David M. Green, and John A. Swets, also in 1954.
[4] Detection theory was used in 1966 by John A. Swets and David M. Green for psychophysics.
[5] Green and Swets criticized the traditional methods of psychophysics for their inability to discriminate between the real sensitivity of subjects and their (potential) response biases.
[6] Detection theory has applications in many fields such as diagnostics of any kind, quality control, telecommunications, and psychology.
The concept is similar to the signal-to-noise ratio used in the sciences and confusion matrices used in artificial intelligence.
Signal detection theory (SDT) is used when psychologists want to measure the way we make decisions under conditions of uncertainty, such as how we would perceive distances in foggy conditions or during eyewitness identification.
[7][8] SDT assumes that the decision maker is not a passive receiver of information, but an active decision-maker who makes difficult perceptual judgments under conditions of uncertainty.
In foggy circumstances, we are forced to decide how far away from us an object is, based solely upon visual stimulus which is impaired by the fog.
To apply signal detection theory to a data set where stimuli were either present or absent, and the observer categorized each trial as having the stimulus present or absent, the trials are sorted into one of four categories: Based on the proportions of these types of trials, numerical estimates of sensitivity can be obtained with statistics like the sensitivity index d' and A',[9] and response bias can be estimated with statistics like c and β.
[10] Signal detection theory can also be applied to memory experiments, where items are presented on a study list for later testing.
Signal Detection Theory has wide application, both in humans and animals.
Topics include memory, stimulus characteristics of schedules of reinforcement, etc.
Conceptually, sensitivity refers to how hard or easy it is to detect that a target stimulus is present from background events.
In contrast, having to remember 30 words rather than 5 makes the discrimination harder.
[6] Bias is the extent to which one response is more probable than another, averaging across stimulus-present and stimulus-absent cases.
Bias can be desirable if false alarms and misses lead to different costs.
In contrast, giving false alarms too often (crying wolf) may make people less likely to respond, a problem that can be reduced by a conservative response bias.
The objective of compressed sensing is to recover high dimensional but with low complexity entities from only a few measurements.
The number of measurements needed in the recovery of signals is by far smaller than what Nyquist sampling theorem requires provided that the signal is sparse, meaning that it only contains a few non-zero elements.
There are different methods of signal recovery in compressed sensing including basis pursuit, expander recovery algorithm[11], CoSaMP[12] and also fast non-iterative algorithm.
In other words, measurement matrices must satisfy certain specific conditions such as RIP (Restricted Isometry Property) or Null-Space property in order to achieve robust sparse recovery.
Taking this approach minimizes the expected number of errors one will make.
For example, if an alarm goes off, indicating H1 (an incoming bomber is carrying a nuclear weapon), it is much more important to shoot down the bomber if H1 = TRUE, than it is to avoid sending a fighter squadron to inspect a false alarm (i.e., H1 = FALSE, H2 = TRUE) (assuming a large supply of fighter squadrons).
The Bayes criterion approach is to maximize the expected utility:
Das and Geisler [15] extended the results of signal detection theory for normally distributed stimuli, and derived methods of computing the error rate and confusion matrix for ideal observers and non-ideal observers for detecting and categorizing univariate and multivariate normal signals from two or more categories.