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摘要暂缺

线性回归中线性后验期望对正态分布的刻画AI 解读

We consider the general linear model Y = Aβ + ε in the Bayesian framework and examine the implications of the statement that the posterior expectation of β, given Y, is a linear function of Y. Under various conditions on the model, it is shown that this linear posterior expectation implies that both β and ε are normally distributed. For most of the practical situations in which linear models are used, only normal distributions have linear posterior expectations.

线性回归中线性后验期望对正态分布的刻画AI 解读

We consider the general linear model Y = Aβ + ε in the Bayesian framework and examine the implications of the statement that the posterior expectation of β, given Y, is a linear function of Y. Under various conditions on the model, it is shown that this linear posterior expectation implies that both β and ε are normally distributed. For most of the practical situations in which linear models are used, only normal distributions have linear posterior expectations.

配对关系丢失的随机样本中相关系数的估计AI 解读

Inference about the correlation coefficient $\rho$ in a bivariate normal distribution is considered when observations from the distribution are available only in the form of a broken random sample. In other words, a random sample of $n$ pairs is drawn from the distribution but the observed data are only the first components of the $n$ pairs and, separately, some unknown permutation of the second components of the $n$ pairs. Under these conditions, the estimation of $\rho$ is,…

摘要暂缺

顺其自然：将尾部面积解释为后验概率或似然比AI 解读

Consider a problem in which a certain statistic X has a specified distribution function F(x) if a given hypothesis H is true, and suppose that the hypothesis H is evaluated by calculating the tail area 1 – F(x) corresponding to the observed value x of the statistic X. Examples are given in which this tail area is equal to the posterior probability that H is true and in which it is equal to the likelihood ratio comparing H to a certain class K of alternatives. The purpose of…

摘要暂缺