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...

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

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...

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...

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...

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

neighbour classifier guarantees an error rate of no worse than twice the Bayes error rate (the minimum achievable error rate given the distribution of the...

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)...

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...

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...

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...

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

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

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...

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

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

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

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

Discovery Rate in Statistical Problems. April, 2001 (Section 3.2, Page 51) Other Sources Zhao, Zhigen; Hwang, J. T. Gene (2012). "Empirical Bayes false coverage...

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...

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...

respect to decision a also minimizes the overall Bayes Risk. This optimal decision, a* is known as the Bayes (decision) Rule - it minimises the average loss...

answer around .7. The correct answer according to Bayes' theorem is closer to .97 ( based on Bayes' theorem: 0.7 8 × 0.3 4 0.7 8 × 0.3 4 + 0.3 8 × 0.7...