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广义尼罗河问题：参数函数的稳健置信集AI 解读

The pivotal model is described and applied to the estimation of parametric functions $\phi(\theta)$. This leads to equations of the form $H(x; \theta) = G\{p(x, \theta)\}$. These can be solved directly or by the use of differential equations. Examples include various parametric functions $\phi(\theta, \sigma)$ in a general location-scale distribution $f(p), p = (x - \theta)/\sigma$ and in two location-scale distributions. The latter case includes the ratio of the two scale…

最小二乘法的逻辑基础AI 解读

SUMMARY Two alternative modes of developing the logic of the least squares theorem are presented. The first is based on the mean square error, the second on a notion of restricted sufficiency.

控制图与随机过程AI 解读

Summary A new approach to control charts for industrial processes is suggested, based on the idea that the underlying stochastic process should be specified, its parameters estimated, and the control procedure related to these. Optimum estimators are derived, and practical approximations to these are indicated.

概率与统计史研究之九：Thomas Bayes《论机会学中一个问题的求解》AI 解读

Bayes's paper, reproduced in the following pages, must rank as one of the most famous memoirs in the history of science and the problem it discusses is still the subject of keen controversy. The intellectual stature of Bayes himself is measured by the fact that it is still of scientific as well as historical interest to know what Bayes had to say on the questions he raised. And yet such are the vagaries of historical records, that almost nAothing is known about the personal…

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