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正态情形下后验均值的收缩AI 解读

Bayes estimation with a normal conditional distribution and an unknown prior distribution is considered. It is shown that the posterior mean always shrinks the observation toward a local maximum of the marginal distribution of the observation. For any symmetric, unimodal prior distribution itis shown that the posterior mean lies between the observation and the prior mean.

二项数据的贝叶斯方法AI 解读

A Bayesian procedure is obtained for the simultaneous estimation of the parameters of m binomial distributions. The method uses logistic transformations for the parameters and an exchangeable prior distribution. Information is combined between the binomial distributions to obtain estimates which, under certain circumstances, will be superior to the usual proportions. This paper is intended as a forerunner to a more general theory for the analysis of nonlinear models.

一种非参数经验贝叶斯估计量AI 解读

An empirical Bayes procedure introduced by Lemon & Krutchkoff (1969) is generalized to eliminate the need for knowledge of the conditional distribution. The procedure is then discussed from a non-Bayesian point of view.

常规统计问题中非正常先验贝叶斯推断的反贝叶斯后果AI 解读

For two routine statistical problems, inference about the ratio of two exponential means and inference about the coefficient of variation of a normal random variable, a serious pathology of Bayesian inference based on improper priors is uncovered and investigated.

经验贝叶斯方法与标准治疗的重复使用AI 解读

The fact that more is generally known about a standard treatment in a clinical trial than about the test treatment is exploited in empirical Bayes estimates based on the results of using the same standard in other trials. Such estimates are proposed for the case of dicho-tomous response, and discussed in terms of an example in cancer research.

一种连续经验贝叶斯平滑技术AI 解读

Maritz (1966) and Lemon & Krutchkoff (1969) each describe discrete empirical Bayes smoothing techniques. These techniques essentially attempt to approximate the prior distribution function. Here a continuous smoothing technique which is based on a smooth and continuous approximation to the prior density function is presented. Results from a Monte Carlo study of the Poisson distribution are reported which show that the continuous smoothing technique has desirable small-sample…

向量观测的经验贝叶斯估计：Stein 方法的扩展AI 解读

The statistician is considering several independent normal linear models with identical structures, and desires to estimate the vector of unknown parameters in each of them. An estimator is constructed which dominates the usual Gauss-Markov estimator in terms of total squared error loss. This estimator is shown to have good efficiency in the Bayesian situation where the parameter vectors themselves have a normal prior distribution. A practical example is given.

正态分布标准差与方差比的最短区间表AI 解读

Tables are presented for Bayes shortest posterior intervals on the standard deviation and variance ratio of normal distributions. A general procedure for obtaining such intervals is reviewed, and a discussion of frequentist shortest intervals is given along with frequentist interpretations of the intervals from these tables.

限制贝叶斯与经验贝叶斯估计量的风险：第一部分，贝叶斯情形AI 解读

The first part of this article considers the Bayesian problem of estimating the mean, θ, of a normal distribution when the mean itself has a normal prior. The usual Bayes estimator for this situation has high risk if θ is far from the mean of the prior distribution. We suggest rules which do not have this bad property and still perform well against the normal prior. These rules are compromises between the Bayes rule and the MLE. Similar rules are suggested for the empirical…

正态分布标准差与方差比的最短区间表AI 解读

Tables are presented for Bayes shortest posterior intervals on the standard deviation and variance ratio of normal distributions. A general procedure for obtaining such intervals is reviewed, and a discussion of frequentist shortest intervals is given along with frequentist interpretations of the intervals from these tables.

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参数具有马尔可夫结构的经验贝叶斯问题AI 解读

A study is made of an empirical Bayes estimation problem in which the set of parameter values is a realization of a stationary Markov chain. The Bayes rule is derived as a function of the transition probabilities of the Markov chain. The performance of empirical Bayes rules, which use estimates of these transition probabilities based on the observations, is investigated by simulation. Two other rules are shown to be competitors of the empirical Bayes rules in some particular…

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摘要暂缺

调查抽样回归推断的贝叶斯、信赖与频率学派视角AI 解读

Summary In this paper an attempt is made to show how the regression analysis generally used for hypothetical populations can also be validated for the actual populations commonly dealt with in statistical surveys. This validation is based on a frequency distribution generated by randomization. In this context some comments are made on the relationships between Bayes, fiducial and frequency theories of statistical inference.

对数正态分布与对数正态回归的贝叶斯及非贝叶斯分析AI 解读

In this article, Bayesian and non-Bayesian methods for estimating parameters of the log-normal distribution and of log-normal regression processes are considered. Posterior distributions for parameters of interest are derived and their properties are described. With respect to point estimation, a rather broad class of estimators is defined and, relative to this class, new minimal mean square error (MSE) estimators for the median and mean of the log-normal distribution and…

对数正态分布与对数正态回归的贝叶斯及非贝叶斯分析AI 解读

In this article, Bayesian and non-Bayesian methods for estimating parameters of the log-normal distribution and of log-normal regression processes are considered. Posterior distributions for parameters of interest are derived and their properties are described. With respect to point estimation, a rather broad class of estimators is defined and, relative to this class, new minimal mean square error (MSE) estimators for the median and mean of the log-normal distribution and…

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最优线性估计量的经验贝叶斯版本及二项分布应用AI 解读

An empirical Bayes estimator is one which estimates the posterior mean by making use of past data. For certain conditional distributions though, no empirical Bayes estimator can be found which converges to the posterior mean as past data are accumulated. However, an optimal linear estimator for a parameter, say θ1 can often be found. This optimal linear estimator depends upon the first two prior moments, both of which can often be estimated. The resulting estimator has been…

相关随机效应分析：含两个随机分量的线性模型AI 解读

Linear regression models with two random components, one of which is time correlated, are analysed from a Bayesian viewpoint. The problem of making inferences about the parameters when the time correlated component is stationary is discussed. Necessary modifications needed for nonstationary and explosive models are indicated. The analysis is illustrated by a numerical example showing that the time series component of the data can exert a strong influence in determining the…

非正态分布的后验精度AI 解读

Summary The result “average posterior precision equals or exceeds prior precision plus average observation precision” is proved for any distributions of a single variable. The “average” used is in effect a harmonic mean.