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# Kernel (statistics)

The term kernel has several distinct meanings in statistics. [1]

## Bayesian inference

Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as evidence is acquired.

## Bayesian statistics

Bayesian statistics is a subset of the field of statistics in which the evidence about the true state of the world is expressed in terms of degrees of belief or, more specifically, Bayesian probabilities.

## Cluster analysis

Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense or another) to each other than to those in other groups (clusters).

## Conditional expectation

In probability theory, the conditional expectation of a random variable is another random variable equal to the average of the former over each possible "condition".

## Conjugate prior

In Bayesian probability theory, if the posterior distributions p(θ|x) are in the same family as the prior probability distribution p(θ), the prior and posterior are then called conjugate distributions, and the prior is called a conjugate prior for the likelihood function.

## Density estimation

In probability and statistics, density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function.

## Indicator function

In mathematics, an indicator function or a characteristic function is a function defined on a set X that indicates membership of an element in a subset A of X, having the value 1 for all elements of A and the value 0 for all elements of X not in A. It is usually denoted by a bold or blackboard bold 1 symbol with a subscript describing the event of inclusion.

## Integrable system

In mathematics and physics, there are various distinct notions that are referred to under the name of integrable systems.

## Kernel (statistics)

The term kernel has several distinct meanings in statistics.

## Kernel density estimation

In statistics, kernel density estimation (KDE) is a non-parametric way to estimate the probability density function of a random variable.

## Kernel method

In machine learning, kernel methods are a class of algorithms for pattern analysis, whose best known member is the support vector machine (SVM).

## Kernel regression

The kernel regression is a non-parametric technique in statistics to estimate the conditional expectation of a random variable.

## Kernel smoother

A kernel smoother is a statistical technique for estimating a real valued function f(X)\,\,\left(X\in \mathbb^ \right) by using its noisy observations, when no parametric model for this function is known.

## Logistic distribution

In probability theory and statistics, the logistic distribution is a continuous probability distribution.

## Machine learning

Machine learning is a subfield of computer sciencehttp://www.britannica.com/EBchecked/topic/1116194/machine-learning that evolved from the study of pattern recognition and computational learning theory in artificial intelligence.

## Markov kernel

In probability theory, a Markov kernel (or stochastic kernel) is a map that plays the role, in the general theory of Markov processes, that the transition matrix does in the theory of Markov processes with a finite state space.

## Multivariate kernel density estimation

Kernel density estimation is a nonparametric technique for density estimation i.e., estimation of probability density functions, which is one of the fundamental questions in statistics.

## Nonparametric statistics

Nonparametric statistics are statistics not based on parameterized families of probability distributions.

## Normal distribution

In probability theory, the normal (or Gaussian) distribution is a very common continuous probability distribution.

## Normalizing constant

The concept of a normalizing constant arises in probability theory and a variety of other areas of mathematics.

## Parameter

A parameter (from the Ancient Greek παρά, "para", meaning "beside, subsidiary" and μέτρον, "metron", meaning "measure"), in its common meaning, is a characteristic, feature, or measurable factor that can help in defining a particular system.

## Point process

In statistics and probability theory, a point process is a type of random process for which any one realisation consists of a set of isolated points either in time or geographical space, or in even more general spaces.

## Probability density function

In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value.

## Probability distribution

In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.

## Probability mass function

In probability theory and statistics, a probability mass function (pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value.

## Pseudo-random number sampling

Pseudo-random number sampling or non-uniform pseudo-random variate generation is the numerical practice of generating pseudo-random numbers that are distributed according to a given probability distribution.

## Random variable

In probability and statistics, a random variable, aleatory variable or stochastic variable is a variable whose value is subject to variations due to chance (i.e. randomness, in a mathematical sense).

## Real-valued function

In mathematics, a real-valued function or real function is a function whose values are real numbers.

## Regression analysis

In statistics, regression analysis is a statistical process for estimating the relationships among variables.

## Reproducing kernel Hilbert space

In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space (RKHS) is a Hilbert space associated with a kernel that reproduces every function in the space or, equivalently, where every evaluation functional is bounded.

## Sign (mathematics)

In mathematics, the concept of sign originates from the property of every non-zero real number to be positive or negative.

## Spectral density

The power spectrum of a time series x(t) describes how the variance of the data x(t) is distributed over the frequency domain, into spectral components which the series x(t) may be decomposed.

## Spectral density estimation

In statistical signal processing, the goal of spectral density estimation (SDE) is to estimate the spectral density (also known as the power spectral density) of a random signal from a sequence of time samples of the signal.

## Statistical classification

In machine learning and statistics, classification is the problem of identifying to which of a set of categories (sub-populations) a new observation belongs, on the basis of a training set of data containing observations (or instances) whose category membership is known.

## Statistics

Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data.

## Time series

A time series is a sequence of data points, typically consisting of successive measurements made over a time interval.

## Window function

In signal processing, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval.

## References

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