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However, in most fielded systems, unwanted clutter and interference sources mean that the noise level changes both spatially and temporally. In this case, a changing threshold can be used, where the threshold level is raised and lowered to maintain a constant probability of false alarm. This is known as constant false alarm rate (CFAR) detection.
Since V is a random variable and is a constant (), the false positive ratio is also a random variable, ranging between 0–1. The false positive rate (or "false alarm rate") usually refers to the expectancy of the false positive ratio, expressed by (/).
The degree to which the observer tolerates false alarms to achieve a higher rate of detection is termed the bias. Bias represents a strategy to minimize the consequences of missed targets and false alarms. As an example, the lookout during a bank robbery must set a threshold for how "cop-like" an approaching individual or vehicle may be.
The probability of type I errors is called the "false reject rate" (FRR) or false non-match rate (FNMR), while the probability of type II errors is called the "false accept rate" (FAR) or false match rate (FMR). If the system is designed to rarely match suspects then the probability of type II errors can be called the "false alarm rate". On the ...
An estimate of d′ can be also found from measurements of the hit rate and false-alarm rate. It is calculated as: d′ = Z(hit rate) − Z(false alarm rate), [15] where function Z(p), p ∈ [0, 1], is the inverse of the cumulative Gaussian distribution. d′ is a dimensionless statistic. A higher d′ indicates that the signal can be more ...
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).
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Using the sequential analysis ("online") approach, any change test must make a trade-off between these common metrics: False alarm rate; Misdetection rate; Detection delay; In a Bayes change-detection problem, a prior distribution is available for the change time. Online change detection is also done using streaming algorithms.