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Are two Classifiers performing equally? A treatment using Bayesian Hypothesis Testing
Related concepts (39)
Naive Bayes classifier
In statistics, naive Bayes classifiers are a family of simple "probabilistic classifiers" based on applying Bayes' theorem with strong (naive) independence assumptions between the features (see Bayes classifier). They are among the simplest Bayesian network models, but coupled with kernel density estimation, they can achieve high accuracy levels. Naive Bayes classifiers are highly scalable, requiring a number of parameters linear in the number of variables (features/predictors) in a learning problem.
Statistical hypothesis testing
A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. While hypothesis testing was popularized early in the 20th century, early forms were used in the 1700s. The first use is credited to John Arbuthnot (1710), followed by Pierre-Simon Laplace (1770s), in analyzing the human sex ratio at birth; see .
Null hypothesis
In scientific research, the null hypothesis (often denoted H0) is the claim that no relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative relationship does not exist, hence the term "null". In addition to the null hypothesis, an alternative hypothesis is also developed, which claims that a relationship does exist between two variables.
Set theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory.
Set (mathematics)
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics.
Likelihood-ratio test
In statistics, the likelihood-ratio test assesses the goodness of fit of two competing statistical models, specifically one found by maximization over the entire parameter space and another found after imposing some constraint, based on the ratio of their likelihoods. If the constraint (i.e., the null hypothesis) is supported by the observed data, the two likelihoods should not differ by more than sampling error. Thus the likelihood-ratio test tests whether this ratio is significantly different from one, or equivalently whether its natural logarithm is significantly different from zero.
Empty set
In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set. Any set other than the empty set is called non-empty. In some textbooks and popularizations, the empty set is referred to as the "null set".
Sequential analysis
In statistics, sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data are evaluated as they are collected, and further sampling is stopped in accordance with a pre-defined stopping rule as soon as significant results are observed. Thus a conclusion may sometimes be reached at a much earlier stage than would be possible with more classical hypothesis testing or estimation, at consequently lower financial and/or human cost.
Sewage treatment
Sewage treatment (or domestic wastewater treatment, municipal wastewater treatment) is a type of wastewater treatment which aims to remove contaminants from sewage to produce an effluent that is suitable to discharge to the surrounding environment or an intended reuse application, thereby preventing water pollution from raw sewage discharges. Sewage contains wastewater from households and businesses and possibly pre-treated industrial wastewater. There are a high number of sewage treatment processes to choose from.
Wastewater treatment
Wastewater treatment is a process which removes and eliminates contaminants from wastewater and converts this into an effluent that can be returned to the water cycle. Once returned to the water cycle, the effluent creates an acceptable impact on the environment or is reused for various purposes (called water reclamation). The treatment process takes place in a wastewater treatment plant. There are several kinds of wastewater which are treated at the appropriate type of wastewater treatment plant.