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线性回归预测中的实验选择AI 解读

Bayesian decision theory is used to obtain optimal designed and random regression experiments. If a choice is possible, it is shown how to decide between them. This is done if the data obtained are to be analysed in order that a future values of the dependent variable can be predicted using the best subset of the independent variables.

贝叶斯分类的渐近结果AI 解读

We have a population composed of two subpopulations whose probability properties are described by known univariate distribution functions, $G(x)$ and $H(x)$, respectively. The probability of observing an individual from the first population is $\theta$, from the second is $1 - \theta$. We assume $\theta$ is a random variable with a prior distribution on (0, 1) and find the Bayes rule for classifying $n$ observations as from $G$ or from $H$ when the loss function is equal to…

一般线性假设下系数估计与模型选择的后验一致性AI 解读

Berk (1970), LeCam (1953) and others have given conditions for the consistency of posterior distributions from a sequence of random variables. They have required that the sequence be i.i.d. We show that their results, Berk's in particular, may be extended to the general linear hypothesis with normal errors model (where the sequence of observations of the dependent variable need not be i.i.d.). We do not assume that the distribution governing the sequence of dependent…

贝叶斯点估计量的抽样性质AI 解读

The sampling distributions of various Bayesian point estimators are examined and it is shown that by choosing an appropriate prior distribution for the unknown parameter such estimators can be less biased than the maximum likelihood estimator. It is also shown that a pivotal quantity can be developed by a suitable transformation of the unknown parameter.

通过部件测试估计系统可靠性的最优抽样方案（一）：固定样本量AI 解读

A Bayesian decision theoretic approach is employed to compare sampling schemes designed to estimate the reliability of series and parallel systems by testing individual components. Quadratic loss is assumed and schemes are found which minimize Bayes risk plus sampling cost. Several kinds of initial information concerning the reliability of the individual components, all of which assume the components function independently, are considered. The case for which the initial…

随机参数估计的递归解AI 解读

Some applications of the Wiener-Kolmogorov and Bayes approaches are discussed with regard to the construction of recursive equations for the best linear estimator of a stochastic parameter. Solutions are given for the prediction, filtering and smoothing cases when the parameter follows a vector Markov process and is observed with error. The Bayes solution is used to generate a canonical factorization of the autocovariance generating function of the observed series.…

贝叶斯点估计量的抽样性质AI 解读

The sampling distributions of various Bayesian point estimators are examined and it is shown that by choosing an appropriate prior distribution for the unknown parameter such estimators can be less biased than the maximum likelihood estimator. It is also shown that a pivotal quantity can be developed by a suitable transformation of the unknown parameter.

随机参数估计的递归解AI 解读

Some applications of the Wiener-Kolmogorov and Bayes approaches are discussed with regard to the construction of recursive equations for the best linear estimator of a stochastic parameter. Solutions are given for the prediction, filtering and smoothing cases when the parameter follows a vector Markov process and is observed with error. The Bayes solution is used to generate a canonical factorization of the autocovariance generating function of the observed series.…

先验分布未完全指定时的贝叶斯推断AI 解读

The G-minimax decision criterion is criticized from a Bayesian viewpoint, and an alternative hybrid decision criterion with a more satisfactory rationale is suggested.

贝叶斯检验与贝叶斯风险的渐近行为AI 解读

In this paper the asymptotic behaviors of the Bayes test and Bayes risk are studied in both the one-sided and two-sided testing problems, where the independent observations are taken from one member of a one-parameter exponential family. Precise asymptotic expressions are found which show the Bayes procedure to be relatively insensitive to the prior distribution as the sample size increases to infinity.

错误知识模型下选择题评分的经验贝叶斯方法AI 解读

This article develops multiple-choice test scoring rules, concentrating on Bayes rules and their frequency theory analogs, empirical Bayes rules. Conditions are given for empirical Bayes estimates to lie in the probability simplex. The misinformation model is considered in detail. It is shown that ranking by raw scores is equivalent to ranking by Bayes scores when the loss function increases with error and the sampling distribution has the monotone likelihood ratio property.…

用交叉验证确定回归模型的样本量AI 解读

A cross-validation approach to the a priori determination of sample size requirements and the a posteriori estimates of the validity of a derived regression equation is developed for regression models, where sampling from multivariate normal populations is discussed in particular. Tables of sample size estimates are presented for the random model and their applications illustrated. An algorithm is given to obtain tables for the fixed model directly from those for the random…

对“未决定”受访者进行推断的贝叶斯方法AI 解读

This article is concerned with the survey problem of estimating category probabilities when some of the subjects respond to sensitive questions in the “don't know,” “no opinion” or “undecided” category, to avoid stating their true beliefs. The suggested approach draws on the information obtained from subjects who respond in unambiguous categories on the main question of interest, and on subsidiary questions posed to the same subjects (possibly in the same survey). This…

错误认知模型下多项选择题评分的经验贝叶斯方法AI 解读

This article develops multiple-choice test scoring rules, concentrating on Bayes rules and their frequency theory analogs, empirical Bayes rules. Conditions are given for empirical Bayes estimates to lie in the probability simplex. The misinformation model is considered in detail. It is shown that ranking by raw scores is equivalent to ranking by Bayes scores when the loss function increases with error and the sampling distribution has the monotone likelihood ratio property.…

摘要暂缺

回归分析中的岭型估计量AI 解读

Summary An examination of the mean-square error properties of a class of shrinkage estimators for the normal regression model leads to a new derivation of the Hoerl–Kennard (1970) Ridge estimator and its generalization. Comparison is made with the James–Stein estimator, and with the generalized-inverse estimator proposed by Marquardt (1970). A Bayesian approach is noted.

单侧贝叶斯区间与频率学派置信区间不相容的一则说明AI 解读

Summary With a proper prior distribution the one-sided Bayes confidence interval for the scalar parameter θ in the density function f(x, θ) never coincides with the corresponding confidence interval based on frequency, whether the experiment is of fixed sample size or sequential.

The problem of estimating powers of the variance of a normal distribution is considered when loss is essentially squared error. A class of minimax estimators is found by extending the techniques of Stein. It is shown, at least for estimating the variance, that a subclass of the above consists of generalized Bayes estimators.

改进等变估计量的方法AI 解读

Techniques for improving on equivariant estimators are described. They may be applied, although without assurance of success, whatever be the family of underlying distributions. The loss function is required to satisfy an intuitively reasonable condition but is otherwise arbitrary. One of these techniques amounts to a sample space, orbit-by-orbit analysis of the conditional expected loss given the orbit. It yields, when successful, a "testimator". A second technique obtains…

Lehmann 备择下两样本问题的贝叶斯分析AI 解读

A Bayesian analysis of the two-sample problem under the Lehmann alternatives is considered. This analysis is based on the rank order statistic. Comparisons are made with Savage's rank test.

用于计算机辅助疾病鉴别诊断的离散多元密度估计AI 解读

A Bayesian approach is taken to the problem of estimating a multivariate discrete density. Prior distributions on the space of multivariate densities are formulated to reflect the idea that the density is near a particular one, or near one which has independent variates. Given a sample of multivariate observations, an approximation to the posterior distribution of the unknown density is developed, and simple formulae for a density which approximates the mode of this…

概率密度的启发式估计AI 解读

A heuristic procedure related to hypothesis testing is offered as a practical alternative to Bayesian estimation of probability densities. Although closely related to the ‘window’ method, it overcomes some of the problems associated with that technique. The proposed method is computationally rapid and easy to use.

An approximate method is suggested for evaluating the decision rules of Watson (1974) for situations where only a partial specification of the prior distribution can be given. The method is applied to the problem of estimating the mean of a distribution of unknown form, under quadratic loss.

列联表独立性的贝叶斯因子AI 解读

The null hypothesis of row-column independence in a two-way contingency table can be expressed as a constraint on the parameters in various standard statistical sampling models. Four sampling models are considered, which are related by nested conditioning. By having the prior distribution in any one model induce the prior distribution in each further conditioned model, it is shown that the Bayes factors for independence will factorize, and there by expose the evidence…