Kernel (statistics)

The term kernel is used in statistical analysis to refer to a window function. The term 'kernel' has several distinct meanings in different branches of statistics.Support: | u | ≤ 1 {displaystyle |u|leq 1} 'Boxcar function'Support: | u | ≤ 1 {displaystyle |u|leq 1} (parabolic)Support: | u | ≤ 1 {displaystyle |u|leq 1} Support: | u | ≤ 1 {displaystyle |u|leq 1} Support: | u | ≤ 1 {displaystyle |u|leq 1} Support: | u | ≤ 1 {displaystyle |u|leq 1} Support: | u | ≤ 1 {displaystyle |u|leq 1} The term kernel is used in statistical analysis to refer to a window function. The term 'kernel' has several distinct meanings in different branches of statistics. In statistics, especially in Bayesian statistics, the kernel of a probability density function (pdf) or probability mass function (pmf) is the form of the pdf or pmf in which any factors that are not functions of any of the variables in the domain are omitted. Note that such factors may well be functions of the parameters of the pdf or pmf. These factors form part of the normalization factor of the probability distribution, and are unnecessary in many situations. For example, in pseudo-random number sampling, most sampling algorithms ignore the normalization factor. In addition, in Bayesian analysis of conjugate prior distributions, the normalization factors are generally ignored during the calculations, and only the kernel considered. At the end, the form of the kernel is examined, and if it matches a known distribution, the normalization factor can be reinstated. Otherwise, it may be unnecessary (for example, if the distribution only needs to be sampled from).