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完全相干推断AI 解读

In a general setting in which prior distributions that may take on the value $\infty$ are admitted, an inference based on a posterior for a prior, $\mu$, that is "minimally compatible" with the inference is shown to have a strong property of expectation consistency, that implies a corresponding property of coherence: A nonnegative expected payoff function for a gambler's strategy is necessary 0 almost everywhere $(\mu)$. In the converse direction, under appropriate…

基于正交级数的单变量密度估计AI 解读

Orthogonal series estimators of univariate densities are proposed that are derived from and motivated by kernel estimators optimal in Whittle's (1958) sense. A preliminary fit of the data from within a one or two parameter class of densities plays the role of a prior mean density. The ratio of the true density and the prior mean density is assumed to have a series expansion in terms of functions orthogonal with respect to the prior mean density. Coefficients of terms of the…

利用正交级数估计一元概率密度AI 解读

Orthogonal series estimators of univariate densities are proposed that are derived from and motivated by kernel estimators optimal in Whittle's (1958) sense. A preliminary fit of the data from within a one or two parameter class of densities plays the role of a prior mean density. The ratio of the true density and the prior mean density is assumed to have a series expansion in terms of functions orthogonal with respect to the prior mean density. Coefficients of terms of the…

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两个随机序变量分布的最大似然估计AI 解读

The maximum likelihood estimates and Ĝ of two distribution functions F and G are found, subject to the restrictions that for all x and that and Ĝ are of the discrete type. Random samples x 1, ···, x m and y 1, ···, y n are taken from the respective distributions and these m+n values are ordered according to magnitude, with x's before y's in cases of equality. These n+m values are divided into a number of “strings” as follows. The first string ends after the y value that is…