论文检索

摘要暂缺

矩阵加权平均与后验界AI 解读

Summary Bounds for matrix weighted averages of pairs of vectors are presented. The weight matrices are constrained to certain classes suggested by the Bayesian analysis of the linear regression model and the multivariate normal model. The bounds identify the region within which the posterior location vector must lie if the prior comes from a certain class of priors.

连续单参数指数族的单调经验贝叶斯检验AI 解读

Let $\theta$ be the natural parameter of a continuous one-parameter exponential family. An empirical Bayes test is constructed for testing $\theta \leqq 0$ against $\theta > 0$ with a piecewise linear loss function. Since the problem is monotone, Bayes tests for a given prior distribution can be characterized by a single parameter, e.g., the size of the test under $\theta = 0$. Therefore the construction of an empirical Bayes test can be reduced to the construction of an…

后验分布的 Bernstein–von Mises 近似AI 解读

It is shown that under certain regularity conditions the Bernstein-v. Mises approximation of the posterior distributions is of order $O(n^{-\\frac{1}{2}})$ with high probability.

序贯检验的渐近效率AI 解读

Some concepts of relative and absolute efficiency for sequential tests are considered. These are sequential analogs of Hodges-Lehmann and Chernoff efficiencies. Using these criteria, several sequential tests for the mean of a normal distribution are evaluated. Among them are Wald's SPRT, Anderson's triangular boundary, Bayes and APO tests and a repeated significance test. Truncated versions of these tests are also considered. Asymptotic expressions for the (expected)…

近似后验分布AI 解读

This paper proposes the use of approximate posterior distributions resulting from operational prior distributions chosen with regard to the realized likelihood function. L.J. Savage's “precise measurement” is generalized for approximation in terms of an arbitrary operational prior density, including mixed-type prior distributions with positive probabilities on singular subsets. A new approximation is also given relating such distributions to absolutely continuous…

摘要暂缺

后验联合众数与边际众数AI 解读

Posterior joint modes have often been used as point estimators in Bayesian applications to avoid laborious numerical integration of complicated posterior densities. We present methods facilitating the straightforward computation of posterior marginal modes in a wide variety of models, and discuss whether marginal modes provide better approximations than joint modes to the posterior means.

摘要暂缺

渐近最优的序贯贝叶斯区间估计程序AI 解读

A theory of sequential Bayes interval estimation procedures for a single parameter is developed for the case where the loss for using an interval $I$ is a linear combination of the length of $I$, the indicator of noncoverage of $I$, and the number of observations taken. A class of stopping rules $\{t(c): c > 0\}$ is shown to be asymptotically pointwise optimal (A.P.O.) and asymptotically optimal (A.O.) for the confidence interval problem as the cost $c$ per observation tends…

扰动协方差矩阵未知时的系数先验信息AI 解读

usefulness of prior information. Viewed broadly, this theme has encompassed such diverse topics as the estimation of a system of simultaneous structural equations, the specification and estimation of distributed lags, and the formal integration of stochastic prior and sample information through Bayes' theorem. Without exception, the results have encouraged the incorporation of further prior information into our statistical procedures, in the sense that the judicious use of…

方差齐性的贝叶斯检验AI 解读

An alternative test of homogeneity of variances in samples from normal populations is developed. The performance of Bartlett's test and the new test proposed here is compared to the F-test in the case of two samples. The performance of Bartlett's test is not particularly good when samples are of unequal sizes, whereas the proposed test performs well for both equal and unequal sample sizes.

平衡三阶段嵌套随机效应模型中方差分量估计量的均方误差比较AI 解读

Various estimators of variance components for the balanced three-stage nested random effects model are compared under standard assumptions of normality and independence of random effects, using MSE as the measure of performance. Several results are proven, demonstrating the inequality relationships on MSE of the unbiased, restricted maximum likelihood and maximum likelihood, and several modifications of the unbiased and maximum likelihood estimators as introduced here,…

由贝叶斯检验规则导出的区间估计AI 解读

Given a family of rules for the three-decision testing problems of locating a scalar parameter θ relative to θ0, with decisions θ < θ0, θ = θ0 and θ > θ0, and given a sample x, the set S(x) = {θ0: decide θ = θ0) (usually an interval) is an intuitively appealing set estimate of θ. This paper considers the optimality of S(x) for the case in which the testing rules are Bayes. The main result is that when the losses for the testing problems have a particular structure, S(x) is…

贝叶斯回归中的缺失变量（二）AI 解读

We are concerned with the problem of parameter estimation in normal regression when some of the observations are missing. A Bayesian approach with vague prior distributions is taken. No assumption is made about the independent variables for which no observations are missing, but the missing components are assumed to be normally distributed with a mean that can depend on the other variables. Joint estimators of the parameters are obtained as the joint mode of the posterior…

多元 Student-t 误差回归模型的贝叶斯与非贝叶斯分析AI 解读

The linear multiple regression model is analyzed assuming the error vector has a multivariate Student-t distribution with zero location vector and scalar dispersion matrix; the multivariate Cauchy and normal distributions are special cases. It is found that the usual least squares coefficient estimate is the maximum likelihood estimate and the mean of the posterior distribution under a diffuse prior distribution. Inferences based on usual t- and F-statistics are shown valid…

方差齐性的贝叶斯检验AI 解读

An alternative test of homogeneity of variances in samples from normal populations is developed. The performance of Bartlett's test and the new test proposed here is compared to the F-test in the case of two samples. The performance of Bartlett's test is not particularly good when samples are of unequal sizes, whereas the proposed test performs well for both equal and unequal sample sizes.

由贝叶斯检验规则导出的区间估计AI 解读

Given a family of rules for the three-decision testing problems of locating a scalar parameter θ relative to θ0, with decisions θ < θ0, θ = θ0 and θ > θ0, and given a sample x, the set S(x) = {θ0: decide θ = θ0) (usually an interval) is an intuitively appealing set estimate of θ. This paper considers the optimality of S(x) for the case in which the testing rules are Bayes. The main result is that when the losses for the testing problems have a particular structure, S(x) is…

摘要暂缺

贝叶斯回归中的缺失变量（二）AI 解读

We are concerned with the problem of parameter estimation in normal regression when some of the observations are missing. A Bayesian approach with vague prior distributions is taken. No assumption is made about the independent variables for which no observations are missing, but the missing components are assumed to be normally distributed with a mean that can depend on the other variables. Joint estimators of the parameters are obtained as the joint mode of the posterior…

分布函数的经验贝叶斯估计AI 解读

A sequence of empirical Bayes estimators is defined for estimating a distribution function. The sequence is shown to be asymptotically optimal relative to a Ferguson Dirichlet process prior. Exact risk expressions are derived and the rate, at which the overall expected loss approaches the minimum Bayes risk, is exhibited. The empirical Bayes approach, based on the Dirichlet process, is also applied to the problem of estimating the mean of a distribution.

经验贝叶斯程序的渐近最优性AI 解读

The purpose of this paper is to obtain weaker sufficient conditions than those given by Robbins [6] for the asymptotic optimality of empirical Bayes procedures. In so doing a general method for providing asymptotic optimality is given which because of its simplicity should prove quite useful not only for the empirical Bayes problem but for other related asymptotic problems as well. Three areas of application are indicated herein.

摘要暂缺

von Mises–Fisher 分布的贝叶斯推断AI 解读

The main aim of this note is to give a theoretical discussion of Bayesian inference for the von Mises-Fisher distribution. The choice of particular priors is considered and the admissibility of certain Bayesian estimators studied. For the multisample case estimators are given. Some problems of testing hypotheses are summarized in the form of posterior odds against the null hypothesis.