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指数分布参数的一类序贯检验AI 解读

Weiss [5] and Freeman and Weiss [2] have shown how to construct sampling plans which at least approximately minimize the maximum expected sample size in the case of Bernoulli and Normal populations. In this paper we construct sequential procedures of this type for the testing of an exponential parameter. An invariance property of the stopping region is presented which simplifies the construction of the Bayes regions. Several sampling plans are given and some of their…

行内观测序列相关的双向固定效应方差分析AI 解读

This paper considers a Bayesian approach to the two-way analysis of variance when the error terms within rows are not independent, but have a covariance matrix dependent on at most two unknown parameters. The posterior density for a linear contrast of row means is obtained. The robustness of the procedure to different priors on the serial correlation coefficient is also discussed.

正态混合分布的成分估计AI 解读

The problem of estimating the components of a mixture of two normal distributions, multivariate or otherwise, with common but unknown covariance matrices is examined. The maximum likelihood equations are shown to be not unduly laborious to solve and the sampling properties of the resulting estimates are investigated, mainly by simulation. Moment estimators, minimum χ2 and Bayes estimators are discussed but they appear greatly inferior to maximum likelihood except in the…

两种终端决策与多阶段抽样下贝叶斯决策规则的渐近性质（一）AI 解读

Summary The model is based on a differentiable prior distribution, a linear loss function, an asymptotically normal sampling distribution and sampling costs proportional to the sample size. Asymptotic expressions are derived for sample sizes, acceptance and rejection criteria and the minimum regret by minimizing the average regret for a k-stage sampling and decision procedure. The results generalize previously known results for k = 1 and 2 and bridge the gap to sequential…

线性贝叶斯方法AI 解读

Summary A method of linear prediction is proposed, which follows the Bayesian scheme in combining prior and present information, but which uses only the first two moments of the distribution of parameters and observations, rather than the complete probability model required of Bayesian techniques.

复合决策与经验贝叶斯AI 解读

Summary The analysis of a sequence of decision problems of identical structure is considered, and the similarities and differences between the compound decision and empirical Bayes approaches explored. The paper includes a brief review of the literature and examines the criteria which have been used in comparing compound decision and empirical Bayes procedures with conventional methods. The performance of one of these procedures is examined in detail, and the previously…

多阶段调查中的估计AI 解读

A superpopulation model is proposed for two-stage sampling from a finite population and we consider the problem of estimating a linear function of the finite population elements. We find the estimate with smallest mean squared error among linear estimates with bounded mean squared error without any assumption about the form of the super-population distribution. If the superpopulation is assumed to be normal this estimate is the mean of the posterior distribution. The…

多元线性回归模型中的经验贝叶斯估计量AI 解读

Empirical Bayes estimators for the parameters in the general linear regression model are presented. These estimators by-pass exact knowledge of the prior distribution of the parameters by means of supplementary information from similar independent experiments. Indexing quantities are obtainned which summarize the information containe in a typical experimental situation, an Monte Carlo simulation is employed to determine the degree of mean square improvement of empirical…

一种经验贝叶斯平滑技术AI 解读

Empirical Bayes procedures generally require the estimation of marginal probabilities. Maritz (1996) showed that the usual estimator for a discrete probability smoothing the estimators of discrete probabilities. Here we present a general procedure for smoothing probabilities and apply it to the Poisson situation.

摘要暂缺

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…

二乘二列联表的精确贝叶斯分析与 Fisher 精确显著性检验AI 解读

Summary A relationship is derived between the posterior probability of negative association of rows and columns of a 2 × 2 contingency table and Fisher's “exact” probability, as given in existing tables for testing the hypothesis of no association of rows and columns. The result for the 2 × 2 table is generalized to provide the posterior probability that one discrete-valued random variable is stochastically larger than another.

信赖论证及其在调查抽样中的应用AI 解读

Summary Sprott (1960) proposed certain restrictions on distributions a posteriori in terms of the likelihood function. Hacking (1965) put forward a criterion for irrelevance restricting the choice of the pivots in terms of the likelihoods. This paper presents an extended application of Hacking's criterion to accommodate ancillary statistics. This extension is utilized to obtain the fiducial distribution of the mean of a survey (finite) population based on the given random…

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…

复合多项分布与有限总体分类数据的贝叶斯分析AI 解读

A Bayesian analysis of the parameter vector, W (Wj = number of elements in category j), of a multivariate hypergeometric distribution is considered. It is shown that if, a priori, W is compound multinomial (CMtn), then, a posteriori, W is a translated CMtn. Many properties of the CMtn distribution are derived. These include joint moments of all orders; a characterization in terms of independent compound Poisson variables, conditional distribution of one subvector given…

摘要暂缺

点估计中的若干经验贝叶斯方法AI 解读

In point estimation with a squared-error loss function the Bayes estimator is the posterior mean. In the empirical Bayes approach we must construct a consistent sequence of estimators for this posterior mean using past experience. This construction is done here for four general families of conditional distributions which include as special cases: the Poisson, the gamma, the normal and the uniform.

特征根与特征向量的贝叶斯估计：以二元正态分布为重点AI 解读

This paper discusses from a Bayesian viewpoint some aspects of the estimation of latent roots and vectors of the covariance matrix of the bivariate normal distribution. The joint distribution of (i) the angle of the canonical transformation, and (ii) the ratio of the larger root to the total variance is considered in detail and illustrated by an example. Also discussed is the problem of making inferences about the larger roots, and several simple approximations to the…

后验分布的渐近行为AI 解读

Summary Let a random sample of size n be taken from a distribution having a density depending on a real parameter θ, and let θ have an absolutely continuous prior distribution with density π(θ). We give a rigorous proof that, under suitable regularity conditions, the posterior distribution of θ will, when n tends to infinity, be asymptotically normal with mean equal to the maximum-likelihood estimator and variance equal to the reciprocal of the second derivative of the…

最小二乘理论的基础AI 解读

Summary The Bayesian theory of least squares is founded upon a weaker and more tangible form of prior knowledge than the conventional assumption of normality. The underlying assumption is a form of conditional uniformity on spheres for the “actual errors” in the experiment. This provides a unified theory appropriate for randomization models in the analysis of variance as well as for classical least-squares analysis.

行内观测序列相关的双向固定效应方差分析AI 解读

This paper considers a Bayesian approach to the two-way analysis of variance when the error terms within rows are not independent, but have a covariance matrix dependent on at most two unknown parameters. The posterior density for a linear contrast of row means is obtained. The robustness of the procedure to different priors on the serial correlation coefficient is also discussed.

利用随机分配控制选择偏差AI 解读

In comparing two treatments, suppose the suitable subjects arrive sequentially and must be treated at once. In such situations, if the experiment calls for fixed treatment numbers, the experimenter can, using his knowledge of the number of treatments that have been assigned, bias the experiment by his selection of subjects. If we consider the method of assigning treatments as an experimental design, Blackwell & Hodges (1957) have shown that the minimax design is the…

正态混合分布成分的估计AI 解读

The problem of estimating the components of a mixture of two normal distributions, multivariate or otherwise, with common but unknown covariance matrices is examined. The maximum likelihood equations are shown to be not unduly laborious to solve and the sampling properties of the resulting estimates are investigated, mainly by simulation. Moment estimators, minimum χ2 and Bayes estimators are discussed but they appear greatly inferior to maximum likelihood except in the…

多元线性回归模型中的经验贝叶斯估计AI 解读

Empirical Bayes estimators for the parameters in the general linear regression model are presented. These estimators by-pass exact knowledge of the prior distribution of the parameters by means of supplementary information from similar independent experiments. Indexing quantities are obtainned which summarize the information containe in a typical experimental situation, an Monte Carlo simulation is employed to determine the degree of mean square improvement of empirical…