Binary classification ($Y\in \{0,1\}$)

Classification in statistical learning with two possible labels. Given the conditional probability $\eta (x)=\mathbb{P}(Y=1\mid X=x)$, a Bayes classifier under zero-one loss predicts one exactly when $\eta (x)\ge 1/2$, with arbitrary decisions at ties.

A plot of classification precision against classification recall as a threshold changes. An uninformative ranking has expected precision equal to the positive prevalence. Comparisons should retain the same evaluation population or explicitly account for changed prevalence.

The fraction of genuinely positive cases recovered by a classifier. The denominator counts all reference-positive cases, $TP+FN$, rather than positive predictions. In a diagnostic setting this is diagnostic sensitivity.

The fraction of predicted positives that are genuinely positive. It depends on prevalence as well as the true positive rate and false positive rate.

A plot of true positive rate against false positive rate while a decision threshold varies over a fixed evaluation population. A random ranking has an expected diagonal curve; a perfect ranking reaches the upper-left corner.

The integral of the receiver operating characteristic's true positive rate with respect to its false positive rate. Equivalently, the probability that a randomly selected positive is ranked above a randomly selected negative, with half weight for ties. It measures discrimination rather than probability calibration or utility at a particular threshold.

Two subsets of a Euclidean space are weakly linearly separable when a hyperplane with nonzero normal vector places them in opposite closed half-spaces. Points on the separating hyperplane may belong to either subset. Strict separation instead requires strictly opposite signs, excluding all boundary ties.

Diagnostic specificity is the probability that a test is negative in someone without the target condition. For an antibody test, relevant negative controls can include samples with antibodies to related pathogens to assess cross-reactivity. With true positive fraction $p$, observed positivity is $Sep+(1-Sp)(1-p)$.

Diagnostic sensitivity is the probability that a test is positive in a person who has the target condition. For past-infection assays, the target is prior infection rather than current disease. Estimate it from suitable independently characterized positive samples; using the same assay to define truth would make the assessment circular.

The false positive rate is $\mathbb{P}(\text{positive result}\mid \text{truly negative class})$. In screening, it measures erroneous positives among genuinely disease-free individuals.