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以给定一般指数族为共轭先验族的抽样模型AI 解读

Let $\mathscr{K} = \{K_\lambda: \lambda \in \Lambda\}$ be a family of sampling distributions for the data $x$ on a sample space $\mathscr{X}$ which is indexed by a parameter $\lambda \in \Lambda,$ and let $\mathscr{F}$ be a family of priors on $\Lambda$. Then $\mathscr{F}$ is said to be conjugate for $\mathscr{K}$ if it is closed under sampling, that is, if the posterior distributions of $\lambda$ given the data $x$ belong to $\mathscr{F}$ for almost all $x$. In this paper,…

线性指数族中的保符号无偏估计量AI 解读

Let ω G∈ Ω be a distribution parameter and r(ω) a positive estimand with range r(Ω). Hoeffding (1984) called an estimator that takes values only in r(Ω), including the boundaries of r(Ω), a range-preserving estimator. The range-preserving property is a sensible requirement to impose on an estimator. If we require unbiasedness, however, such estimators become difficult to find. In this article a less constraining condition, namely sign-preserving unbiasedness, is considered.…

修正二项模型下的 Dorfman 型群组检测AI 解读

In this article we introduce a new group-testing model which we refer to as the modified binomial model. This new model, when applicable, not only requires a smaller per unit expected number of tests to identify all units (in a population of dichotomous units) than does the frequently considered binomial model, but also is always preferable to individual testing. We consider optimal Dorfman-type procedures under the modified model and present methods for determining the best…

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