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Detection theory

Signal Detection Theory: – Signal detection theory measures the ability to differentiate between information-bearing patterns and noise. – Signal recovery in electronics separates patterns from […]

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Signal Detection Theory:
– Signal detection theory measures the ability to differentiate between information-bearing patterns and noise.
– Signal recovery in electronics separates patterns from the background.
– Determiners affect how a detecting system will detect a signal.
– Factors like experience, expectations, and physiological state can affect detection thresholds.
– Early work in detection theory was done by radar researchers.
– SDT in psychology measures decision-making under uncertainty.
– Witness decisions in eyewitness identifications are based on perceived familiarity.
– Applications of Signal Detection Theory in memory, reinforcement schedules, etc.
– Measures and calculations related to signal detection theory.
– Development of signal detection theory for detecting signals.
– Studies on visual detection and target detection.
– Application in eyewitness identification and criminal justice accuracy.

Sensitivity and Discriminability:
– Sensitivity refers to how easy it is to detect a target stimulus.
– Sensitivity index is a commonly used statistic for computing sensitivity.
– Area under the ROC-curve is a non-parametric measure of sensitivity.
– Longer study time makes discrimination easier.
– More items to remember make discrimination harder.

Bias:
– Bias is the probability of one response over another.
– Bias is independent of sensitivity.
– Liberal response bias may be desirable in certain situations.
– Conservative response bias can reduce false alarms.
– Bias can be affected by the cost of misses and false alarms.

Compressed Sensing:
– Compressed sensing aims to recover high-dimensional signals from few measurements.
– It is used for recovering sparse signals with low complexity.
– Methods include basis pursuit, CoSaMP, and fast non-iterative algorithms.
– Measurement matrices must satisfy conditions like RIP for robust sparse recovery.
– Compressed sensing is closely related to signal detection theory.
– Efficient and robust compressed sensing methods.
– CoSaMP algorithm for signal recovery from incomplete samples.
– Fast noniterative algorithm for compressive sensing.
– Use of binary measurement matrices in compressive sensing.

Mathematics in Detection Theory:
– MAP testing involves choosing between hypotheses based on observations.
– Classical approach involves choosing the hypothesis with higher a posteriori probability.
– Equal a posteriori probabilities may lead to choosing a single choice or random selection.
– A priori probabilities play a role in decision-making.
– Mathematics in detection theory involves decision-making based on probabilities.
– Bayes Criterion importance in responding appropriately to different scenarios.
– Results extended for detecting and categorizing signals.
– Various studies and publications on signal detection theory.

Detection theory (Wikipedia)

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.

According to the theory, there are a number of determiners of how a detecting system will detect a signal, and 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. 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.

Much of the early work in detection theory was done by radar researchers. By 1954, the theory was fully developed on the theoretical side as described by Peterson, Birdsall and Fox and the foundation for the psychological theory was made by Wilson P. Tanner, David M. Green, and John A. Swets, also in 1954. Detection theory was used in 1966 by John A. Swets and David M. Green for psychophysics. 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.

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.

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