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面向第二阶段最佳表现优化的子集选择AI 解读

In the search for the best of n candidates, two-stage procedures of the following type are in common use. In a first stage, weak candidates are removed, and the subset of promising candidates is then further examined. At a second stage, the best of the candidates in the subset is selected. In this article, optimization is not aimed at the parameter with largest value but rather at the best performance of the selected candidates at Stage 2. Under a normal model, a new…

同时检验中的 Γ 极小极大选择程序AI 解读

Suppose we have to decide on the basis of appropriately drawn samples which of $k$ treatment populations are "good" compared to either given control values or to a control population from which an additional sample is available. The unknown parameters are assumed to vary randomly according to a prior distribution about which we only have the partial knowledge that it is contained in a given class $\Gamma$ of priors. Though we derive in both cases (under the assumption of…

基于检验的识别与选择程序AI 解读

Let $X_1, \cdots, X_k$ be independent random variables with distributions $Q_1, \cdots, Q_k$ defined on a common range space $(\mathscr{X}, \mathscr{G})$. At the beginning it is assumed that the $Q_i$ are known but not the pairing with the $X_i$, and the goal is to identify the $X_i$ which comes from $Q_1$. First it is shown that every procedure based on a total ordering in $\mathscr{X}$ can be viewed as being based on (the $p$-value of) a test for deciding between $H_0: \{Q_1\}$…