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总体均值后验期望的一则札记AI 解读

Summary It is a well-known result, see for example Lindley (1965) and Raiffa and Schlaifer (1961), that if x̄ is the mean of a sample of independent observations distributed N(μ, σ2) where σ2 is known, and if μ has been assigned a normal prior distribution, N(m, v), then the posterior expectation of μ, given the sufficient statistic x̄, has the form {x̄(n/σ2) + m/v}/{(n/σ2)+1/v}, that is, has the intuitively appealing form of a weighted average of the prior mean and sample…

有限总体抽样中的主观贝叶斯模型AI 解读

Summary A general and basic model for inference about characteristics of a finite population of distinguishable elements is presented from a subjectivistic–Bayesian point of view. A subjectivist analogue to simple random sampling, based on the notion of exchangeable random variables, is discussed and the inputs and assumptions underlying the model are shown to involve nothing more than is required for inference under Bayesian models for infinite populations. The model is…

利用先验信息进行分层与多阶段抽样的最优分配AI 解读

The author [1], [2] has given an algorithm for finding that stratified allocation which minimizes the posterior variance of the overall population mean subject to a budget constraint under a model in which a normal prior distribution and independent normal sampling distributions were assumed. The budget constraint assumed a variable per unit cost of observation. In the present paper these results are extended to cover the case where there are fixed costs, as well as variable…

摘要暂缺

存在无应答时的最优样本设计AI 解读

Discussed here are several aspects of a simple model for dealing with nonresponse. The model is, in a sense, a sequential one and is developed from a Bayesian decision theory point of view. Within this framework we examine how formalization and combination of one's opinions, past experience, and “objective” evidence concerning the proportion of non-respondents, the differences and relations between respondents and nonrespondents, the cost of obtaining information from…

非信息性停止规则下推断差异的一个例子AI 解读

Raiffa & Schlaifer (1961) cite an example of discrepancies in inference which may result from use of inferential methods which violate the likelihood principle by their dependence on non-informative stopping rules. In this note we give a simple and realistic example of the dependence of minimum variance unbiased estimators on non-informative stopping rules.