In statistical classification, Bayes error rate is the lowest possible error rate for any classifier of a random outcome (into, for example, one of two...

Error rate, meaning the frequency of errors, can have the following uses: Bayes error rate Bit error rate Per-comparison error rate Residual bit error...

the Bayes classifier is optimal and Bayes error rate is minimal proceeds as follows. Define the variables: Risk R ( h ) {\displaystyle R(h)} , Bayes risk...

Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting conditional probabilities, allowing...

Bayes classifier – Classification algorithm in statistics Bayes discriminability index Bayes error rate – Error rate in statistical mathematics Bayes...

maximum (Bayes-optimal) discriminability index for two distributions, based on the amount of their overlap, i.e. the optimal (Bayes) error of classification...

The Bhattacharyya distance can be used to upper and lower bound the Bayes error rate: 1 2 − 1 2 1 − 4 ρ 2 ≤ L ∗ ≤ ρ {\displaystyle {\frac {1}{2}}-{\frac...

algorithm is guaranteed to yield an error rate no worse than twice the Bayes error rate (the minimum achievable error rate given the distribution of the data)...

integrated out. Empirical Bayes methods can be seen as an approximation to a fully Bayesian treatment of a hierarchical Bayes model. In, for example, a...

as an error of the second kind. In terms of the courtroom example, a type II error corresponds to acquitting a criminal. The crossover error rate (CER)...

Despite the use of Bayes' theorem in the classifier's decision rule, naive Bayes is not (necessarily) a Bayesian method, and naive Bayes models can be fit...

or liability that are not analyzable as errors in base rates or Bayes's theorem. An example of the base rate fallacy is the false positive paradox (also...

In statistics, the false discovery rate (FDR) is a method of conceptualizing the rate of type I errors in null hypothesis testing when conducting multiple...

rate Baseball statistics Basu's theorem Bates distribution Baum–Welch algorithm Bayes classifier Bayes error rate Bayes estimator Bayes factor Bayes linear...

In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value...

complement of the type II error rate (i.e., one minus the type II error rate). Precision is related to the type I error rate, but in a slightly more complicated...

(as true positive rate and true negative rate are); they depend also on the prevalence. Both PPV and NPV can be derived using Bayes' theorem. Although...

multiple comparisons problem that controls the strong-sense family-wise error rate (this claim has been disputed). It improves on the power of Bonferroni...

the Bayes optimal classifier represents a hypothesis that is not necessarily in H {\displaystyle H} . The hypothesis represented by the Bayes optimal...

A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a...

compensate for the number of inferences being made. Methods for family-wise error rate give the probability of false positives resulting from the multiple comparisons...

the error variance of the regression model. Mathematics portal Brier score Coefficient of determination Constant false alarm rate Detection error tradeoff...

(corresponding to the lowest error). Momentum both speeds up the learning (increasing the learning rate) when the error cost gradient is heading in the...

inference Bayes' theorem Bayes estimator Prior distribution Posterior distribution Conjugate prior Posterior predictive distribution Hierarchical bayes Empirical...

then some special e-variables can be written as Bayes factors with some very special priors, but most Bayes factors one encounters in practice are not e-variables...

This list of U.S. states and territories by poverty rate covers the 50 U.S. states, the District of Columbia, and the territory of Puerto Rico. Referenced...

{\displaystyle \alpha } is the type I error rate (false positives) and β {\displaystyle \beta } is the type II error rate (false negatives); the statistical...

Double Data Rate Synchronous Dynamic Random-Access Memory (DDR SDRAM) is a type of synchronous dynamic random-access memory (SDRAM) widely used in computers...

Bayesian inference (/ˈbeɪziən/ BAY-zee-ən or /ˈbeɪʒən/ BAY-zhən) is a method of statistical inference in which Bayes' theorem is used to calculate a probability...

this goal "is not attainable". Aldrich, J (2008). "R. A. Fisher on Bayes and Bayes' theorem". Bayesian Analysis. 3 (1): 161–170. doi:10.1214/08-BA306...