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Concept
Receiver operating characteristic
Summary
A receiver operating characteristic curve, or ROC curve, is a graphical plot that illustrates the diagnostic ability of a binary classifier system as its discrimination threshold is varied.
The ROC curve is the plot of the true positive rate (TPR) against the false positive rate (FPR), at various threshold settings.
The ROC can also be thought of as a plot of the power as a function of the Type I Error of the decision rule (when the performance is calculated from just a sample of the population, it can be thought of as estimators of these quantities). The ROC curve is thus the sensitivity or recall as a function of fall-out.
Given the probability distributions for both true positive and false positive are known, the ROC curve is obtained as the cumulative distribution function (CDF, area under the probability distribution from to the discrimination threshold) of the detection probability in the y-axis versus the CDF of the false positive probability on the x-axis.
ROC analysis provides tools to select possibly optimal models and to discard suboptimal ones independently from (and prior to specifying) the cost context or the class distribution. ROC analysis is related in a direct and natural way to cost/benefit analysis of diagnostic decision making.
There are a large number of synonyms for components of a ROC curve. They are tabulated on the right.
The true-positive rate is also known as sensitivity, recall or probability of detection. The false-positive rate is also known as probability of false alarm 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 criterion changes.
The ROC curve was first developed by electrical engineers and radar engineers during World War II for detecting enemy objects in battlefields, starting in 1941, which led to its name ("receiver operating characteristic").
It was soon introduced to psychology to account for perceptual detection of stimuli.
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Prevalence
In epidemiology, prevalence is the proportion of a particular population found to be affected by a medical condition (typically a disease or a risk factor such as smoking or seatbelt use) at a specific time. It is derived by comparing the number of people found to have the condition with the total number of people studied and is usually expressed as a fraction, a percentage, or the number of cases per 10,000 or 100,000 people. Prevalence is most often used in questionnaire studies. Incidence (epidemiology)#Incidence vs.
Sensitivity and specificity
Sensitivity and specificity mathematically describe the accuracy of a test that reports the presence or absence of a condition. If individuals who have the condition are considered "positive" and those who do not are considered "negative", then sensitivity is a measure of how well a test can identify true positives and specificity is a measure of how well a test can identify true negatives: Sensitivity (true positive rate) is the probability of a positive test result, conditioned on the individual truly being positive.
Confusion matrix
In the field of machine learning and specifically the problem of statistical classification, a confusion matrix, also known as error matrix, is a specific table layout that allows visualization of the performance of an algorithm, typically a supervised learning one; in unsupervised learning it is usually called a matching matrix. Each row of the matrix represents the instances in an actual class while each column represents the instances in a predicted class, or vice versa – both variants are found in the literature.