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In statistics, when performing multiple comparisons, a false positive ratio (also known as fall-out or false alarm rate [1]) is the probability of falsely rejecting the null hypothesis for a particular test.
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 other hand, if the system is used for validation (and acceptance is the norm) then the FAR is a measure of system security, while the FRR measures user inconvenience level.
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.
The false positive rate (FPR) is the proportion of all negatives that still yield positive test outcomes, i.e., the conditional probability of a positive test result given an event that was not present. The false positive rate is equal to the significance level. The specificity of the test is equal to 1 minus the false positive rate.
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 ...
The true-positive rate is also known as sensitivity or probability of detection. [1] The false-positive rate is also known as the probability of false alarm [1] and equals (1 − specificity). The ROC is also known as a relative operating characteristic curve, because it is a comparison of two operating characteristics (TPR and FPR) as the ...
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).
The positive predictive value (PPV), or precision, is defined as = + = where a "true positive" is the event that the test makes a positive prediction, and the subject has a positive result under the gold standard, and a "false positive" is the event that the test makes a positive prediction, and the subject has a negative result under the gold standard.