Marginal distribution 边缘分布

In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset. It gives the probabilities of various values of the variables in the subset without reference to the values of the other variables. This contrasts with a conditional distribution, which gives the probabilities contingent upon the values of the other variables.

在概率论和统计学中，随机变量集合的一个子集的边缘分布是包含在该子集中的变量的概率分布。它给出了子集中变量的各种值的概率，而不参考其他变量的值。这与条件分布不同，条件分布给出的概率取决于其他变量的值。

Marginal variables are those variables in the subset of variables being retained. These concepts are "marginal" because they can be found by summing values in a table along rows or columns, and writing the sum in the margins of the table.[1] The distribution of the marginal variables (the marginal distribution) is obtained by marginalizing – that is, focusing on the sums in the margin – over the distribution of the variables being discarded, and the discarded variables are said to have been marginalized out.

边缘变量是被保留变量子集中的变量。这些概念是“边缘”概念，因为它们可以通过沿行或列求和表中的值，并在表的页边空白处写上和来找到。【1】边际变量（边际分布）的分布是通过对变量的分布进行边缘化来获得的，也就是说，将重点放在页边空白处的和上。被丢弃的变量被边缘化了。

The context here is that the theoretical studies being undertaken, or the data analysis being done, involves a wider set of random variables but that attention is being limited to a reduced number of those variables. In many applications, an analysis may start with a given collection of random variables, then first extend the set by defining new ones (such as the sum of the original random variables) and finally reduce the number by placing interest in the marginal distribution of a subset (such as the sum). Several different analyses may be done, each treating a different subset of variables as the marginal variables.

本文的背景是，正在进行的理论研究或正在进行的数据分析涉及一组更广泛的随机变量，但这种关注仅限于减少这些变量的数量。在许多应用中，分析可以从一组给定的随机变量开始，然后首先通过定义新的随机变量（如原始随机变量的和）来扩展集合，最后通过关注子集的边际分布（如和）来减少数量。可以进行几个不同的分析，每个分析将不同的变量子集视为边际变量。