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有限总体样本的非参数贝叶斯模型AI 解读

Summary Using Ferguson's (1973) non-parametric priors in a Bayesian analysis of finite populations, we show that asymptotically, at least, the usual estimates and confidence intervals for the population mean in simple and stratified random samples can be justified in Bayesian terms. We then apply these models for estimating population percentiles, and a new procedure for interval estimates in stratified sampling is developed.

多元校准AI 解读

Summary A set of q responses Y = (Y 1 ,…, Yq)T are determined by a set of p explanatory variables x = (X 1,…, Xp)T. A set of l observed vectors Y are available at a single unknown x and it is desired to draw inferences about this unknown vector X. In order to do this calibrating data is available jointly on (Y, X) where two situations are distinguished (i), x is controlled, (ii) x is random. Using orthodox sampling theory on the one hand and Bayesian methods on the other…

模糊先验信息下线性与对数线性模型的贝叶斯因子AI 解读

Summary The Bayes factor, or integrated likelihood ratio, provides a possible Bayesian alternative to the standard F ‐test procedure for comparing two linear models. However, if vague prior information for the model parameters is represented by limiting improper prior forms, it is well known that the resulting Bayes factor involves an arbitrary, unspecified constant, and is thus not well defined. A method of assigning this constant is proposed and illustrated for a number of…

一个有用的经验贝叶斯恒等式AI 解读

For any decision problem, one wishes to find that estimator which minimizes the expected loss. If the loss function is squared error, then the estimator is the mean of the Bayes posterior distribution. Unfortunately the prior distribution may be unknown, but in certain situations empirical Bayes methods can circumvent this problem by using past observations to estimate either the prior or the Bayes estimate directly. Empirical Bayes methods are particularly appealing when…

具有相关残差的多项式趋势分类：贝叶斯方法AI 解读

Three procedures for the classification of multivariate time-dependent data are examined. Two are shown to be Bayes procedures assuming that the time dependence of the data can be described by polynomial regression functions and that the relation among successive residuals is described by a stationary and invertible ARMA process. Relative advantages of these procedures in practical applications and limitations of the model are discussed.

贝叶斯稳健性与 Stein 效应AI 解读

In simultaneous estimation of normal means, it is shown that through use of the Stein effect surprisingly large gains of a Bayesian nature can be achieved, at little or no cost, if the prior information is misspecified. This provides a justification, in terms of robustness with respect to mis-specification of the prior, for employing the Stein effect, even when combining a priori independent problems (i.e., problems in which no empirical Bayes effects are obtainable). To…

具有相关残差的多元多项式趋势分类贝叶斯方法AI 解读

Three procedures for the classification of multivariate time-dependent data are examined. Two are shown to be Bayes procedures assuming that the time dependence of the data can be described by polynomial regression functions and that the relation among successive residuals is described by a stationary and invertible ARMA process. Relative advantages of these procedures in practical applications and limitations of the model are discussed.

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不连续决策过程与门限自回归时间序列建模AI 解读

Setting the problem of approximating an underlying nonlinear time series model within the framework of Bayesian decision theory, we demonstrate how the general analysis of discontinuous decision processes developed by Smith, Harrison & Zeeman (1981) leads naturally to a threshold autoregression.

独立非中心卡方或F检验的合并AI 解读

The problem of combining several independent Chi squared or $F$ tests is considered. The data consist of $n$ independent Chi squared or $F$ variables on which tests of the null hypothesis that all noncentrality parameters are zero are based. In each case, necessary conditions and sufficient conditions for a test to be admissible are given in terms of the monotonicity and convexity of the acceptance region. The admissibility or inadmissibility of several tests based upon the…

多元正态均值最小最大估计量的选择AI 解读

The problem of estimating a $p$-variate normal mean under arbitrary quadratic loss when $p \geq 3$ is considered. Any estimator having uniformly smaller risk than the maximum likelihood estimator $\delta^0$ will have significantly smaller risk only in a fairly small region of the parameter space. A relatively simple minimax estimator is developed which allows the user to select the region in which significant improvement over $\delta^0$ is to be achieved. Since the desired…

使用上下概率进行类贝叶斯决策AI 解读

We consider the use of interval-valued probabilities to represent the support lent to the hypothesis that the parameter value θ lies in a subset A of the parameter set Θ when we observe x, know the likelihoods {fΘ: θεΘ}, and have some prior information concerning the parameter. Our model for prior information is that of a salient prior distribution in which we have little confidence, although we have much less confidence in any alternative prior. We consider notions of…

广义 F 分布的卷积AI 解读

The generalized F variate is the ratio of two independent gamma variates, and its distribution includes as special cases such distributions as the inverted beta, Lomax, and Snedecor's F, Based on convolution, the distribution function of the sum of two independent generalized F variates is derived in terms of a Lauricella-Saran hyper-geometric function of three variables. The results are applied, with numerical examples given, to (a) a Bayesian analysis of the availability…

存在无应答时利用辅助信息的有限总体总量贝叶斯估计AI 解读

This article presents a Bayesian approach to estimation, in a sample survey setting, of a finite population total for some characteristic of interest when nonresponse is present. A general model is described for situations where a Hansen-Hurwitz sampling plan is used. The model makes use of concomitant information that is related both to the characteristic of interest and to the probability of response. A simple example is included to illustrate the usefulness of the…

股票收益风险结构变化的贝叶斯稳健检测AI 解读

In this article we provide a statistical procedure for the analysis of stock market prices that is robust toward departures from the normal distribution assumption and that can detect and evaluate a shift of parameters at an unknown time point. The method is an adaptation of a Bayesian inferential procedure developed by Box and Tiao that allows data to deviate moderately from the normal distribution model. It is applied to a set of U.S. stock market prices for 1971–1974. In…

存在无应答时利用辅助信息进行有限总体总量的贝叶斯估计AI 解读

This article presents a Bayesian approach to estimation, in a sample survey setting, of a finite population total for some characteristic of interest when nonresponse is present. A general model is described for situations where a Hansen-Hurwitz sampling plan is used. The model makes use of concomitant information that is related both to the characteristic of interest and to the probability of response. A simple example is included to illustrate the usefulness of the…

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使用秩似然进行线性模型推断AI 解读

Summary An approximation to the marginal likelihood of the ranks of a set of observations is used to analyse data. The observations, after some arbitrary monotone transformation, are assumed to be independently normally distributed with means related by a linear model. An approximate posterior distribution for the parameters of the linear model is given and used to find predictive distributions for the ordering of future observations. A numerical example is given. Appendices…