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模糊先验信息下非齐次泊松过程的贝叶斯因子AI 解读

SUMMARY The calculation of Bayes factors for rival parametric models of non-homogeneous Poisson processes is considered. If vague prior information for the model parameters is represented by limiting improper prior forms, then the resulting Bayes factor is defined only up to a multiplicative constant. It is noted that the procedure proposed by Spiegelhalter and Smith (1982) does not provide any solution to the problem of assigning the constant if the priors are…

受噪声污染图像的统计分析AI 解读

SUMMARY A continuous two-dimensional region is partitioned into a fine rectangular array of sites or “pixels”, each pixel having a particular “colour” belonging to a prescribed finite set. The true colouring of the region is unknown but, associated with each pixel, there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model. The aim is to reconstruct the true scene, with the additional knowledge that…

单变量时间序列模型识别的贝叶斯程序AI 解读

This paper is concerned with model selection in time series analysis. An identification criterion is presented that is asymptotically equivalent to a Bayes decision rule. The discussion is conducted in the context of a general class of parametric time series models and consideration is given to the special case of order determination in autoregressive moving-average representations. Consistency of the criterion is proved.

外部贝叶斯意见汇总算子的刻画AI 解读

When a panel of experts is asked to provide some advice in the form of a group probability distribution, the question arises as to whether they should synthesize their opinions before or after they learn the outcome of an experiment. If the group posterior distribution is the same whatever the order in which the pooling and the updating are done, the pooling mechanism is said to be externally Bayesian by Madansky (1964). In this paper, we characterize all externally Bayesian…

ε 污染先验下的稳健贝叶斯与经验贝叶斯分析AI 解读

For Bayesian analysis, an attractive method of modelling uncertainty in the prior distribution is through use of $\varepsilon$-contamination classes, i.e., classes of distributions which have the form $\pi = (1 - \varepsilon)\pi_0 + \varepsilon q, \pi_0$ being the base elicited prior, $q$ being a "contamination," and $\varepsilon$ reflecting the amount of error in $\pi_0$ that is deemed possible. Classes of contaminations that are considered include (i) all possible…

非对称损失函数下的贝叶斯估计与预测AI 解读

Estimators and predictors that are optimal relative to Varian's asymmetric LINEX loss function are derived for a number of well-known models. Their risk functions and Bayes risks are derived and compared with those of usual estimators and predictors. It is shown that some usual estimators, for example, a scalar sample mean or a scalar least squares regression coefficient estimator, are inadmissible relative to asymmetric LINEX loss by providing alternative estimators that…

关于平滑先验与非线性回归的一个注记AI 解读

A generalization of a nonparametric estimator proposed by Shiller (1984) is considered. The estimator is shown to be directly related to penalized least squares estimation and spline smoothing. Some simplifications concerning the computation of Shiller's estimator and corresponding posterior covariances are indicated.

摘要暂缺

利用先验信息的自助法AI 解读

Bayesian analysis is subject to the same kinds of misspeciflcation problems which motivate the robustness and nonparametric literature. We present a method of incorporating prior information which performs well without direct knowledge of the error distribution. This is accomplished by replacing the likelihood in Bayes's formula by a bootstrap estimate of the sampling density of a robust estimator. The flexibility of the method is illustrated by examples, and its performance…

摘要暂缺

含变点的泊松过程的贝叶斯分析AI 解读

A Bayesian approach to estimation and hypothesis testing for a Poisson process with a change-point is developed, and an example given.

联立方程系统中单方程估计量的比较AI 解读

Comparisons of estimators are made on the basis of their mean squared errors and their concentrations of probability computed by means of asymptotic expansions of their distributions when the disturbance variance tends to zero and alternatively when the sample size increases indefinitely. The estimators include k -class estimators (limited information maximum likelihood, two-stage least squares, and ordinary least squares) and linear combinations of them as well as…

不等式约束正态线性回归模型的精确推断AI 解读

Abstract Inference in the inequality constrained normal linear regression model is approached as a problem in Bayesian inference, using a prior that is the product of a conventional uninformative distribution and an indicator function representing the inequality constraints. The posterior distribution is calculated using Monte Carlo numerical integration, which leads directly to the evaluation of expected values of functions of interest. This approach is compared with others…

依赖删失模型下基于广义自洽性的生存曲线估计及非参数贝叶斯应用AI 解读

This article presents a family of estimators of the survival function based on right-censored observations which admit the possibility that the censoring variables may not be independent of the true failure variables. This family is obtained by generalizing the self-consistent property (Efron, 1967) of the product limit estimator (Kaplan and Meier, 1958). By assuming a Dirichlet process prior distribution of the observable random vectors, nonparametric Bayesian estimators of…

指数分布分位数估计的容许性与极小极大性AI 解读

The estimation problem of the quantiles $\xi + b\sigma$ of an exponential distribution with unknown location-scale parameter $(\xi, \sigma)$ is considered. We establish the admissibility of the traditional (best equivariant) estimator for quadratic loss when $n^{-1} \leq b \leq 1 + n^{-1}$ where $n$ is the sample size. For $b > 1 + n^{-1}$ a class of minimax procedures is found. This class contains generalized Bayes rules and one of them is shown to be admissible within the…

加权二次损失下多参数伽马分布的同时估计AI 解读

A new class of solutions to a general differential inequality often encountered in multiparameter estimation problems is obtained. Using these solutions as guidelines, improved estimators for the scale parameters as well as the natural parameters of independent gamma distributions are obtained for a large class of weighted quadratic losses. The improved estimators have an empirical Bayes interpretation. They also permit an exact analytical representation of the risk…

指数族混合模型与最小二乘估计量AI 解读

For an arbitrary one parameter exponential family density it is shown how to construct a mixing distribution (prior) on the parameter in such a way that the resulting mixture distribution is a two (or more) parameter exponential family. Reweighted infinitely divisible distributions are shown to be the parametric mixing distributions for which this occurs. As an illustration conditions are given under which a parametric mixture of negative exponentials is in the exponential…

极小极大多重收缩估计AI 解读

For the canonical problem of estimating a multivariate normal mean under squared-error-loss, this article addresses the problem of selecting a minimax shrinkage estimator when vague or conflicting prior information suggests that more than one estimator from a broad class might be effective. For this situation a new class of alternative estimators, called multiple shrinkage estimators, is proposed. These estimators use the data to emulate the behavior and risk properties of…

后验矩与边际密度的精确近似方法AI 解读

This article describes approximations to the posterior means and variances of positive functions of a real or vector-valued parameter, and to the marginal posterior densities of arbitrary (i.e., not necessarily positive) parameters. These approximations can also be used to compute approximate predictive densities. To apply the proposed method, one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima.…

模糊先验信息下对数线性列联表模型的贝叶斯因子札记AI 解读

SUMMARY The approximate Bayes factor, B 01, for log-linear contingency table models proposed by Spiegelhalter and Smith (1982) is indeterminate if any of the cell frequencies is zero. It is noted that use of a standard Jeffreys prior overcomes this difficulty. It is pointed out that – 2 log B 01 is approximately equivalent to Schwarz's (1978) model selection criterion in large samples.

部分线性模型中的样条平滑AI 解读

SUMMARY Suppose that Yi = X'iβ + f(ti) + εi, 1 ≤ i ≤ n, where β, f, and εi are unknown, but the m-th derivative of f is square integrable. Estimates of β and f are given which minimize the sum of the residual sum of squares and a roughness penalty. It is shown that these estimates are Bayes under a diffuse prior on β and f, and that, under mild conditions on Xi, ti, εi, and the roughness penalty, the estimate of β is consistent and asymptotically normal.

使用贝叶斯向量自回归进行预测：五年经验AI 解读

The results obtained in five years of forecasting with Bayesian vector autoregressions (BVAR's) demonstrate that this inexpensive, reproducible statistical technique is as accurate, on average, as those used by the best known commercial forecasting services. This article considers the problem of economic forecasting, the justification for the Bayesian approach, its implementation, and the performance of one small BVAR model over the past five years.

评论：借助 Freedman 式协变量处理无应答问题的贝叶斯视角AI 解读

David Freedman has presented an ingenious and deceptively simple argument that should prove to be of value in many nonrespondent problems. I would like to discuss both the general form of the argument and the specific details from a subjective Bayesian viewpoint, as I believe the argument implicitly involves some delicate questions that are best understood from this viewpoint. The basic structure of Freedman's argument is that although he concedes in general that there may…

经济预测的组合AI 解读

A method for combining forecasts may or may not account for dependence and differing precision among forecasts. In this article we test a variety of such methods in the context of combining forecasts of GNP from four major econometric models. The methods include one in which forecasting errors are jointly normally distributed and several variants of this model as well as some simpler procedures and a Bayesian approach with a prior distribution based on exchangeability of…