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单因素模型中的方差分量推断AI 解读

The estimation of variance components in the one-way model is considered from a subjective Bayesian point of view. The situation in which the classical unbiased estimate of the between variance component is negative is explored in some detail. Exact and approximate posterior distributions are obtained in both the balanced and unbalanced case. Common sense aspects of the problem are emphasized, and some contrasts with other approaches. For example, Bayesianly speaking, a…

逆 Dirichlet 分布及其应用AI 解读

In this paper we obtain a multivariate generalization of the inverted beta distribution. Properties of this distribution and its connection with the multivariate Student-t distribution are discussed. Two asymptotic formulae for approximating the related probability integral are developed and illustrated with numerical examples. Application of this distribution to a problem in Bayesian inference is given.

通过贝叶斯定理推导一类概率分布AI 解读

Summary Being in some respects expository in character, this paper uses Bayes's theorem to derive a k-variate discrete probability distribution which is fundamental inasmuch as it proliferates, under various sets of asymptotic conditions, to yield as its limiting forms an array of other k-variate distributions including the multinomial, independent Poisson, independent negative binomial, independent gamma, Dirichlet and multivariate normal. A systematic arrangement of these…

多元正态分布参数的贝叶斯估计AI 解读

Summary A significant omission from the work of Raiffa and Schlaifer (1961) relating to a multivariate normal distribution is consideration of the case when the dispersion matrix is completely unknown. This paper partially fills the gap by applying the methods of Raiffa and Schlaifer to the particular problems of estimating the mean μ, the dispersion matrix ∑, and the generalized variance | ∑ |, when either or both of μ and ∑ are unknown.

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方差分析中随机效应模型的贝叶斯分析（一）：方差分量后验分布AI 解读

George C. Tiao, W. Y. Tan; Bayesian analysis of random-effect models in the analysis of variance. I. Posterior distribution of variance-components, Biometr

若干贝叶斯与频率学派推断的比较AI 解读

Suppose that we have a sample of observations on a continuous random variable with a distribution depending on one unknown parameter θ. We consider the problem of making inferences about θ when there is no prior information about the value of the parameter. Some examples are discussed for which it is not possible to find Bayesian methods possessing the properties required by frequentist statisticians. The magnitude of the difference between comparable Bayesian and…

贝叶斯视角下回归模型中的预测与决策问题AI 解读

In this paper we review the derivation of the predictive density function for the normal multiple regression model, state and prove a general theorem on optimal point prediction, and show how the predictive density can be employed in the analysis of an illustrative investment problem. Then we derive the predictive density function for the multivariate normal regression model and indicate how it can be used in the analysis of several problems.

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均值与精度均未知的独立多元正态过程的贝叶斯分析AI 解读

Under the assumption that neither the mean vector nor the variance-covariance matrix are known with certainty, the natural conjugate family of prior densities for the multivariate Normal process is identified. Prior-posterior and preposterior analysis is done assuming that the prior is in the natural conjugate family. A procedure is presented for obtaining non-degenerate joint posterior and preposterior distributions of all parameters even when the number of objective sample…

临床试验数据分析的贝叶斯方法AI 解读

A Bayesian logical probability approach is described and its advantages with respect to constructing prior distributions for Bayesian analyses are discussed. Some standard Bayesian distribution theory for categorized data is summarized. Data from an on-going experiment to compare the relative efficacy of four operative treatments for ulcer are used both to pinpoint some of the practical problems involved in clinical trials and to demonstrate the usefulness of Bayesian…

概率预测AI 解读

The posterior distribution for parameters of a data distribution is usually the major objective of a Bayesian statistical analysis. Relatively little attention has been given to the fact that either a prior or a posterior distribution implies a marginal distribution, which may be called a “predictive distribution,” for outcomes of any sample not yet observed. Predictive distributions have been mainly applied to design problems, such as determination of optimal sample size.…

临床试验数据分析的贝叶斯方法AI 解读

A Bayesian logical probability approach is described and its advantages with respect to constructing prior distributions for Bayesian analyses are discussed. Some standard Bayesian distribution theory for categorized data is summarized. Data from an on-going experiment to compare the relative efficacy of four operative treatments for ulcer are used both to pinpoint some of the practical problems involved in clinical trials and to demonstrate the usefulness of Bayesian…

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均一协方差情形下的估计AI 解读

Summary There are three basic methods (confidence, fiducial, Bayesian) of obtaining interval estimates or estimating regions for the parameters of the multivariate normal distribution, none of which need necessarily yield a unique solution, although this has been claimed as a property of the fiducial argument. It has been previously demonstrated that they are not consistent with one another, i.e. they yield different regions for the same parameters. In this paper we show…

误差自相关回归模型的贝叶斯分析AI 解读

In this paper, regression models with error terms generated by a first order autoregressive scheme are analyzed from a Bayesian point of view. Methods are developed for computing posterior distributions of regression coefficients and the parameter of the autoregressive process. The relationship of our approach to sampling theory approaches is briefly discussed.

预测问题中贝叶斯与频率学派方法的比较：贝叶斯容忍域AI 解读

Summary In the theory of statistical tolerance regions, as usually presented in frequentist terms, there are inherent difficulties of formulation, development and interpretation. The present paper re-examines the basic problem from a Bayesian point of view and suggests that such an approach provides a set of widely applicable, mathematically tractable tools, often more tailored to the requirements of users than the corresponding frequentist tools. For the one-dimensional…

多元回归的贝叶斯估计AI 解读

Summary In this paper, we use a Bayesian approach to analyse sets of regression equations with correlated error terms. In the case that the matrix of “independent variables” is the same for all equations, our model reduces to the traditional multivariate regression model. For this case, the marginal posterior distribution of the regression coefficient vector for any equation is shown to be of the multivariate-t form. Further, the variances and covariances of the error terms…

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多元正态分类的后验优势比AI 解读

Summary A class of Bayesian methods is presented for finding the posterior odds or probability that a particular observation belongs to one of k multivariate normal populations. Solutions are given for various assumptions on the parameters of the k populations as well as for known and unknown prior probabilities. An application to genetics is included.

正态分布方差的贝叶斯估计AI 解读

Summary Some new general forms of estimators of the variance of a normal distribution are derived using Bayesian methods, and the conditions under which they lead to previously proposed estimators are discussed.

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投资信托管理质量的变化（？）AI 解读

The paper compares year-to-year changes in the Wiesenberger Index of Return for investment funds of similar objectives. It is initially shown, using correlation techniques, that there was little consistency in yearly performance of the funds during the period from 1951 to 1960. This result serves as support for the assumption that a fund's relative performance in any one year is strictly a random occurrence. We might, therefore, define a “successful” management as one whose…