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二项分布参数的经验贝叶斯估计AI 解读

A smooth empirical Bayes estimator for a binomial parameter is derived. The risk in using this estimator is compared by simulation with that of eight other binomial estimators. For those estimators not having a simple closed form risk, suitable regression equations on the simulation parameters are obtained. These equations are used to identify the regions of superiority of each of the estimators. A numerical example is provided.

以线性回归预测为目标的实验选择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.

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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.

顺其自然：将尾部面积解释为后验概率或似然比AI 解读

Consider a problem in which a certain statistic X has a specified distribution function F(x) if a given hypothesis H is true, and suppose that the hypothesis H is evaluated by calculating the tail area 1 – F(x) corresponding to the observed value x of the statistic X. Examples are given in which this tail area is equal to the posterior probability that H is true and in which it is equal to the likelihood ratio comparing H to a certain class K of alternatives. The purpose of…

具有不完整观测的双变量正态分布的贝叶斯分析AI 解读

We consider the problem of drawing inferences on the difference of the population means when an incomplete sample from a bivariate normal population is available. Whereas Mehta and Gurland [7] have considered this problem from the sampling theory point of view, we tackle here the same problem from a Bayesian approach.

不完整观测下二元正态分布的贝叶斯分析AI 解读

We consider the problem of drawing inferences on the difference of the population means when an incomplete sample from a bivariate normal population is available. Whereas Mehta and Gurland [7] have considered this problem from the sampling theory point of view, we tackle here the same problem from a Bayesian approach.

凸二次回归曲线的贝叶斯估计AI 解读

The estimation of a quadratic regression curve when the quadratic coefficient is known to be positive is treated by a Bayesian method. The method extends easily to deal with a general linear model under parameter constraints.

配对比较实验的贝叶斯分析方法AI 解读

A Bayesian approach to the analysis of paired comparison experiments is presented. Two statistical models are considered: the multibinomial and the Bradley-Terry model. For each, the natural conjugate family of priors is used to represent prior beliefs, and the parameters of the prior are given meaningful interpretations. Two different estimators are suggested for the model parameters, the preference probabilities of the multibinomial model and the worth parameters of the…

共同未知方差下多元正态均值的正规贝叶斯极小极大估计AI 解读

We investigate the problem of estimating the mean vector $\mathbf{\theta}$ of a multivariate normal distribution with covariance matrix equal to $\sigma^2\mathbf{I}_p, \sigma^2$ unknown, and loss $\|\delta - \mathbf{\theta}\|^2/\sigma^2$. We first find a class of minimax estimators for this problem which enlarges a class given by Baranchik. This result is then used to show that for sufficiently large sample sizes (which never need exceed 4) proper Bayes minimax estimators…

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调查设计、对称性与后验分布AI 解读

Summary It is now well known that the sample design is irrelevant in a Bayesian analysis of survey data provided the units are labelled and the sampling is non-informative. However, information about the labels is often not available for the analysis, and in this situation the design will contain information about the labelling and hence affect the inferences. There is one important exception: if the prior distribution is exchangeable and we are interested only in symmetric…

一般贝叶斯线性模型AI 解读

Summary Lindley and Smith (1972), using a hierarchical form of prior structure, derived Bayesian alternatives to least squares estimates for the linear model. This paper examines the Bayesian model in more detail and notes some general properties of the resulting estimators. Comparison is made with a least squares approach to models of the second kind, and an example is given.

用于估计的渐近最优贝叶斯序贯实验设计AI 解读

The purpose of this paper is to find asymptotically optimal Bayes sequential procedures for estimating a function $g(\theta_1, \theta_2,\cdots, \theta_k)$ when there are $k$ experiments $E_1, E_2,\cdots, E_k$ and the performance of the experiment $E_i$ conducts to the observation of a random variable whose distribution depends on the vector parameter $\theta_i$. The term asymptotical refers here to the cost of experimentation tending to zero. The methods used are a…

误差分量回归模型的贝叶斯分析AI 解读

This article examines the use of a two-way, random-effects, model with correlated errors and additional explanatory variables in combining cross-section with time series data. This model has been analyzed from a Bayesian viewpoint. Methods are developed for computing posterior distributions of slope coefficients. The advantage of our approach over sampling theory approaches is briefly discussed. It has been shown how one can obtain reasonable inferences about slope…

威布尔修复过程下的贝叶斯最优大修间隔模型AI 解读

This article presents Bayesian estimators of the parameters of the Weibull hazard function in the restoration process case. These estimators are used in a model which optimizes the interval between machine overhauls. Since the properties of the model are not in closed form, a simulation experiment is used to evaluate the effectiveness of the model. The simulation results show that the model does yield lower machine operating costs than the non-Bayesian approach. The…

二元过程无应答问题的贝叶斯分析AI 解读

A Bayesian treatment is given of a two-phase sampling problem when sampling is from a double dichotomy, losses are quadratic, and sampling costs are linear. The motivating question is: how does one determine an optimal first phase sample from a dichotomous population given that an optimal follow-up sample of nonrespondents in the first phase is to be taken?

Weibull 分布的贝叶斯—信 fiducial 推断AI 解读

Procedures are developed for specifying confidence intervals, from possibly censored data, for any characteristic of a two-parameter Weibull population. Although the methods are formally Bayesian, they have exact relative frequency interpretation for uncensored and Type II censored data. Some simulation results are given to indicate relative frequency behavior for Type 1 censoring, and for comparison to other methods.

误差分量回归模型的贝叶斯分析AI 解读

This article examines the use of a two-way, random-effects, model with correlated errors and additional explanatory variables in combining cross-section with time series data. This model has been analyzed from a Bayesian viewpoint. Methods are developed for computing posterior distributions of slope coefficients. The advantage of our approach over sampling theory approaches is briefly discussed. It has been shown how one can obtain reasonable inferences about slope…

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泊松过程发生率的贝叶斯序贯估计AI 解读

This paper provides numerical and analytical solutions to the problem of estimating the rate of a Poisson process. Optimal designs are obtained for various loss functions and the method of analysis is valid for any other loss function. The cost of sampling plays a fundamental role and since there are many practical situations where there is a time cost and an event cost, a sampling cost per observed event and a cost per unit time are both included.

泊松回归的贝叶斯与经典分析AI 解读

Summary This paper is concerned with the problem of testing the existence of a trend in the means θi of Poisson distributions. It is assumed that these means are changing exponentially, that is, log θi = α + βxi. A classical method is reviewed which is used for testing the hypothesis β = 0. The exact Bayesian distribution for β is derived and a Bayesian approximation suggested which proved to be very useful. Finally, a comparison of these three methods by means of numerical…

合并可能相关的估计问题AI 解读

Summary We have two sets of parameters we wish to estimate, and wonder whether the James-Stein estimator should be applied separately to the two sets or once to the combined problem. We show that there is a class of compromise estimators, Bayesian in nature, which will usually be preferred to either alternative. “The difficulty here is to know what problems are to be combined together— why should not all our estimation problems be lumped together into one grand melée?”…