Binary signal detection theory redirects
We will assume here that the noise distribution is normal. When a signal is added to the noise, the distribution is shifted to the right along the sensory continuum. We can normalize these distributions to simplify and standardize the math involved so that the mean of the noise distribution is zero and the standard deviations of both distributions are 1.
When a subject is presented with the signal at any particular time, the signal will fall along the sensory continuum according to the SN distribution. The subject will base his judgement of detection of the signal according to some criterion along the sensory continuum.
If no signal is presented during a trial the subject is still subject to an event at that time along the sensory continuum which has a probability associated with the N distribution. For any particular trial, the sensory event which may be the result of a signal presentation or no signal presentation is above the criterion level the subject will report seeing the flash. If the sensory event is below the criterion, he will report not seeing the flash.
Let's assume the subjects criterion is located at the point shown in the figure above. If you present the subject with multiple trials in which the signal is presented or not presented there will be a probability associated with the subjects response due to the distributions of the N and SN. In contrast, having to remember 30 words rather than 5 makes the discrimination harder. One of the most commonly used statistics for computing sensitivity is the so-called sensitivity index or d'.
There are also non-parametric measures, such as the area under the ROC-curve. Bias is the extent to which one response is more probable than another. That is, a receiver may be more likely to respond that a stimulus is present or more likely to respond that a stimulus is not present. Bias is independent of sensitivity. For example, if there is a penalty for either false alarms or misses, this may influence bias. If the stimulus is a bomber, then a miss failing to detect the plane may increase deaths, so a liberal bias is likely.
In contrast, crying wolf a false alarm too often may make people less likely to respond, grounds for a conservative bias. The a priori probabilities of H1 and H2 can guide this choice, e. In some cases, it is far more important to respond appropriately to H1 than it is to respond appropriately to H2. The Bayes criterion is an approach suitable for such cases.
Here a utility is associated with each of four situations:. From Wikipedia, the free encyclopedia. Binary classification Constant false alarm rate Decision theory Demodulation Detector radio Estimation theory Just-noticeable difference Likelihood-ratio test Modulation Neyman—Pearson lemma Psychometric function Receiver operating characteristic Statistical hypothesis testing Statistical signal processing Two-alternative forced choice Type I and type II errors.
Signal Recovery from Noise in Electronic Instrumentation 2nd ed. Iterative signal recovery from incomplete and inaccurate samples". Applied and Computational Harmonic Analysis.
Behavior Research Methods, Instruments, and Computers. This article includes a list of references , but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. April Learn how and when to remove this template message. In all of the recovery methods mentioned above, choosing an appropriate measurement matrix using probabilistic constructions or deterministic constructions, is of great importance.
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. Back to the detecting theory, when the detecting system is a human being, characteristics such as experience, expectations, physiological state e.
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.
Much of the early work in detection theory was done by radar researchers. Green, and John A. Swets , also in Swets and David M.
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. It is also usable in alarm management , where it is important to separate important events from background noise.
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. 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.
Since the brightness of the object, such as a traffic light, is used by the brain to discriminate the distance of an object, and the fog reduces the brightness of objects, we perceive the object to be much farther away than it actually is see also decision theory. 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:.
Signal detection theory can also be applied to memory experiments, where items are presented on a study list for later testing. A test list is created by combining these 'old' items with novel, 'new' items that did not appear on the study list. On each test trial the subject will respond 'yes, this was on the study list' or 'no, this was not on the study list'.
Items presented on the study list are called Targets, and new items are called Distractors. Saying 'Yes' to a target constitutes a Hit, while saying 'Yes' to a distractor constitutes a False Alarm.
Signal Detection Theory has wide application, both in humans and animals.