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状态依赖效用AI 解读

Several axiom systems for preference among acts lead to a unique probability and a state-independent utility such that acts are ranked according to their expected utilities. These axioms have been used as a foundation for Bayesian decision theory and subjective probability calculus. In this article we note that the uniqueness of the probability is relative to the choice of what counts as a constant outcome. Although it is sometimes clear what should be considered constant,…

删失回归数据的后验计算AI 解读

This article describes the computation of and sampling from the posterior density for censored regression problems with normal and generalized log-gamma errors. The data augmentation algorithm (Tanner and Wong 1987) is facilitated in the normal error case because of the form of the augmented posterior. In the generalized log-gamma context, this simplicity is absent. The work of Sweeting (1981) is used as a motivation to develop an importance sampling scheme to sample from an…

EM 算法的蒙特卡洛实现与简易数据增广算法AI 解读

The first part of this article presents the Monte Carlo implementation of the E step of the EM algorithm. Given the current guess to the maximizer of the posterior distribution, latent data patterns are generated from the conditional predictive distribution. The expected value of the augmented log-posterior is then updated as a mixture of augmented log-posteriors, mixed over the generated latent data patterns (multiple imputations). In the M step of the algorithm, this…

福利项目质量控制中的统计推断AI 解读

Federal and state agencies estimate rates of payment error made by state caseworkers in determining benefits under the Aid to Families with Dependent Children, Food Stamp, and Medicaid programs. Estimated payment error rates are used in turn to estimate program penalties that are a function of the difference between payment error rates and target rates. This article first outlines the statistical methodology currently used in welfare quality control systems, namely, the…

摘要暂缺

衡量单个观测对贝叶斯因子的影响AI 解读

In this paper we consider a measure of the effect of single observations on a logarithmic Bayes factor defined via the difference in the logarithms of the Bayes factors conditional first on all the data and then omitting an observation. The measure is related to the conditional predictive ordinate. The form of the measure and examples of its use are presented for a variety of situations, normal samples, linear models, log linear models and the checking of distributional…

EM 算法在惩罚似然估计中的应用AI 解读

SUMMARY The EM algorithm is a popular approach to maximum likelihood estimation but has not been much used for penalized likelihood or maximum a posteriori estimation. This paper discusses properties of the EM algorithm in such contexts, concentrating on rates of convergence, and presents an alternative that is usually more practical and converges at least as quickly.

在线性回归模型中结合相关研究与稀疏数据AI 解读

Meta-analysis has become a popular approach for studying systematic variation in parameter estimates across studies. this article discusses the use of meta-analysis results as prior information in a new study. Although hierarchical prior distributions in a traditional Bayesian framework are characterized by complete exchangeability, meta-analysis priors explicitly incorporate heterogeneity in prior vectors. This article discusses the nature of the meta-analysis priors, their…

多元正态均值的主观层次贝叶斯估计：与频率学派的联系AI 解读

In shrinkage estimation of a multivariate normal mean, the two dominant approaches to construction of estimators have been the hierarchical or empirical Bayes approach and the minimax approach. The first has been most extensively used in practice, because of its greater flexibility in adapting to varying situations, while the second has seen the most extensive theoretical development. In this paper we consider several topics on the interface of these approaches,…

指数分布混合假设的检验与混合分布的矩估计AI 解读

This article presents nonparametric methods for testing the hypothesis that duration data can be represented by a mixture of exponential distributions. Both Bayesian and classical tests are developed. A variety of apparently distinct models can be written in mixture of exponentials form. This raises a fundamental identification problem. A consistent estimator for the number of points of support of a discrete mixture is developed. A consistent method-of-moments estimator for…

二项分布参数近似置信区间的准确性AI 解读

This article considers the uniform convergence of the coverage probabilities of some approximate confidence intervals for the binomial parameter p, induced by central limit arguments. A uniform upper bound on the coverage probabilities of any such interval obtained by transformation of the sample proportion [pcirc] n is derived. The coverage probability of the interval induced by the arcsine transformation turns out to be very close to the upper bound. Replacing [pcirc] n by…

估计立法选区重划的选举后果AI 解读

We analyze the effects of redistricting as revealed in the votes received by the Democratic and Republican candidates for state legislature. We develop measures of partisan bias and the responsiveness of the composition of the legislature to changes in statewide votes. Our statistical model incorporates a mixed hierarchical Bayesian and non-Bayesian estimation, requiring simulation along the lines of Tanner and Wong (1987). This model provides reliable estimates of partisan…

估计立法选区重划的选举后果AI 解读

We analyze the effects of redistricting as revealed in the votes received by the Democratic and Republican candidates for state legislature. We develop measures of partisan bias and the responsiveness of the composition of the legislature to changes in statewide votes. Our statistical model incorporates a mixed hierarchical Bayesian and non-Bayesian estimation, requiring simulation along the lines of Tanner and Wong (1987). This model provides reliable estimates of partisan…

比率策略的渐近极小极大性AI 解读

The use of simple random sampling together with ratio estimation is of fundamental importance in survey sampling practice. From a theoretical point of view the ratio estimator has been justified by Bayesian methods (Ericson, 1969) and by superpopulation methods (Royall, 1970). But these methods do not yield a rigorous justification of simple random sampling at the same time. We use the minimax principle in an asymptotic version to justify both simple random sampling and…

两次调查中部分替换单位的连续抽样贝叶斯方法AI 解读

To study time-dependent characteristics of a population, we may sample the same population at regular intervals. A basic problem is how the sample should be selected at different time periods. Here we consider successive sampling with partial replacement of units on two occasions from a Bayesian point of view. Bayes estimators and optimal designs for such priors will be obtained. In one situation, the whole survey, i.e. the first sample and the second sample, is planned…

非正态线性回归：高维显著性水平计算的一个例子AI 解读

Analysis of nonnormal linear models leads to an initial conditioning on the standardized residuals, giving an unnormed density on Rk, where k is the number of parameters. To obtain an observed level of significance for a single parameter it is then necessary to calculate a marginal probability, thus requiring integration in k dimensions. In this paper a conditional approach to evaluating the observed level of significance is developed, and an importance sampling technique is…

摘要暂缺

交叉验证、贝叶斯定理与小样本偏差AI 解读

Researchers in many fields of business are beginning to use cross-validatory techniques to choose between alternative models. In marketing, a Bayesian interpretation of the technique has been proposed. This article examines the Bayesian link in more detail and shows that cross-validatory posterior odds exhibit a systematic departure from exact posterior odds when sample-splitting procedures are employed. Resampling procedures also exhibit a systematic departure when the…

边际尾概率近似与标量参数推断AI 解读

In many situations, inference for a scalar parameter in the presence of nuisance parameters requires integration of either a joint density of pivotal quantities or a joint posterior density. For such inference, accurate approximations of marginal tail probabilities are useful to avoid high-dimensional integrals. Two tail probability approximations are developed in this paper. Numerical results given for conditional inference in location-scale and linear regression models…

基于模型的统计分析的一般框架AI 解读

This paper presents a general framework for model-based statistics. The framework is based on extended concepts of sufficiency and ancillarity. The fundamental theorem of the new theory exhibits in a single equation the reference distributions for decision theory, model checking, and conditional inference for a general statistical model. The theorem includes the equations upon which Bayesian and frequentist statistics are founded. The general theory also fills two gaps…

基于信念函数的先验包络AI 解读

We show that the mathematical structure of belief functions makes them suitable for generating classes of prior distributions to be used in robust Bayesian inference. In particular, the upper and lower bounds of the posterior probability content of a measurable subset of the parameter space may be calculated directly in terms of upper and lower expectations (Theorem 4.1). We also extend an integral representation given by Dempster to infinite sets (Theorem 2.1).

基于部分信息的一致且稳健的位置参数贝叶斯程序AI 解读

We consider Bayes procedures for a location parameter $\theta$ that are robust with respect to the shape of the distribution $F$ of the data. The case where $F$ is fixed (nonrandom) and the case where $F$ has a Dirichlet distribution are both treated. The procedures are based on the posterior distributions of the location parameter given the partial information contained in a robust estimate of location. We show consistency and asymptotic normality of the procedures and give…

平滑样条的平均后验方差与平均平方误差的一致估计AI 解读

A smoothing spline estimator can be interpreted in two ways: either as the solution to a variational problem or as the posterior mean when a particular Gaussian prior is placed on the unknown regression function. In order to explain the remarkable performance of her Bayesian "confidence intervals" in a simulation study, Wahba conjectured that the average posterior variance of a spline estimate evaluated at the observation points will be close to the expected average squared…

二维拉普拉斯平滑的迭代方法及其图像修复应用AI 解读

Smoothing methods are increasingly important in modern graphically oriented data analysis. There are several fast and reliable univariate cross-validated smoothing algorithms, but comparable methods are not available in higher dimensions. This article develops an iterative approach to two-dimensional Laplacian spline smoothing based on tensor-product cubic B splines. Estimating equations are developed and solved iteratively using two-line symmetric successive over relaxation…