Binary signal detection theory redirects
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 noiseconsisting of background stimuli and random activity of the detection machine and of the nervous system of the operator.
In the field of electronicsthe separation of such patterns from a disguising background is referred to as signal recovery. According to the theory, there are a number of determiners of how a detecting system will detect a signal, binary signal detection theory redirects where its threshold levels will be. 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.
Another field which is closely related to signal detection theory is called compressed sensing or compressive sensing. The objective of compressed sensing is to recover high dimensional but with low complexity entities from only a few measurements. Thus, one of the most important applications of compressed sensing is in the recovery of high dimensional signals which are known to be sparse or nearly sparse with only a few linear measurements.
The number of measurements needed in the binary signal detection theory redirects 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 pursuitexpander recovery algorithm CoSaMP  and also fast non-iterative algorithm . 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 binary signal detection theory redirects 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. Swetsalso in Swets and David M. Detection theory has applications in many fields such as diagnostics of any kind, quality controltelecommunicationsand 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 managementwhere 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 binary signal detection theory redirects, 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 binary signal detection theory redirects 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 binary signal detection theory redirects 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 binary signal detection theory redirects 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. Topics include memorystimulus characterists 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.
For example, in a recognition memory paradigm, having longer to study to-be-remembered words makes it easier to recognize previously seen or heard words. 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 binary signal detection theory redirects Type I and type II errors.
Signal Recovery from Noise in Electronic Instrumentation 2nd ed. Iterative signal recovery from incomplete and inaccurate samples".
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The Theory of Signal Detection. The theory of signal detecion was developed by mathematicians and engineers in the 's working in the fields of mathematical statistics and electronic communications. Signal detection deals with the detectability of signals and controlling the criterion that are used for the detection of signals. Early on, it binary signal detection theory redirects apparent that this theory has application to psychophysics because the observer's criterion affects the judgements they make.
The theory of signal detection allows for the ability to separate the effects of the stimulus detectability from the observer's criterion in sensory experiments. The following figure will be used to explain the key concepts we will need for signal detection theory: The subject's task is to detect a signal which is presented along some sensory continuum. For example, the sensory continuum in the binary signal detection theory redirects of the experiment of Hecht, Schlaer and Pirenne, is a visual continuum of flash intensity.
Present in the observers nervous system is noise that may come from a variety of sources such binary signal detection theory redirects spontaneous isomerizations and spontaneous neural discharge. When a signal, a flash in this case, is presented to the subject, in order to detect the flash, the subject must discriminate the signal which is added to the inherant noise from the noise alone.
We think of binary signal detection theory redirects noise as having a distribution; at any binary signal detection theory redirects in time the noise has a value that varies from a mean level. 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 binary signal detection theory redirects 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. These probabilities can be summarized in a conditional probability matrix.
The rows of the matrix represent the presence or absence of a signal and the columns represent the subjects response. If the subject says he saw the signal "yes" when it was present, this is called a hit. If the subject says he didn't see the signal "no" when it was present, this is called a miss. If the subject says he saw the signal "yes" when it was absent, this is called a false alarm. If the subject says he didn't see the signal "no" when it was absent, this is called a correct rejection.
The notation P Y SN means the probability of a yes response given the presentation of the signal and P N N means the probability of a no response given that the signal was absent. So in the example presented here the table would look like this: Notice that the probability sums to 1.
Continue on to Biases and Criterion.