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若干非参数问题的近似贝叶斯解AI 解读

The problem of making inferences about real functions of a probability distribution of unknown form is examined in a Bayesian nonparameteric framework. With respect to a general quadratic loss function, Bayes estimates within the class of linear combinations of a given set of functions on the sample space are obtained for general functions on the distribution space. The result is then used to derive Bayes polynomial estimates of the moments of the distribution.

离散分布的后验概率上界与下界AI 解读

Dempster (1966) defines two sampling models which he labels structures of the first and second types. In this paper we consider the application of the type one model to the problem of finding upper and lower posterior probabilities when sampling from discrete univariate distributions whose suppower consists of the set of noinnegative integers. Specific results are obtained for the Poisson and geometric distributions.

回归误差项的贝叶斯分析AI 解读

Properties of realized regression error terms are studied wherein they are treated as unknown parameters. Posterior distributions for individual realized error terms and for linear and certain quadratic functions of them are derived. Posterior moments of measures of skewness, kurtosis, autocovariance, and autocorrelation, defined in terms of the realized errors, are presented, and selected uses of these results indicated in characterizing properties of realized error terms…

统计分析中的贝叶斯推断AI 解读

Nature of Bayesian Inference Standard Normal Theory Inference Problems Bayesian Assessment of Assumptions: Effect of Non-Normality on Inferences About a Population Mean with Generalizations Bayesian Assessment of Assumptions: Comparison of Variances Random Effect Models Analysis of Cross Classification Designs Inference About Means with Information from More than One Source: One-Way Classification and Block Designs Some Aspects of Multivariate Analysis Estimation of Common…

高阶层级随机效应模型中的贝叶斯等变估计量AI 解读

Summary The Bayes equivariant estimators of the variance components (Zacks, 1970, 1971) are characterized in the case of r-stage hierarchical random effects models when the random effects are normally distributed and are mutually and completely independent. Non-trivial Bayes equivariant estimators are derived using a special prior distribution for the three-stage hierarchical model. It is observed that for the squared error loss function every Bayes equivariant estimator of…

对称狄利克雷先验下反对多项总体等概率的贝叶斯因子AI 解读

A sample $(n_1, n_2,\cdots, n_t)$ is taken from a $t$-category multinomial population. The hypothesis of equiprobability, that the $t$ physical probabilities associated with the cells are all equal to $1/t$, is called the null hypothesis. Conditional on the non-null hypothesis, a symmetric Dirichlet prior of parameter $k$ is assumed $(k \geqq 0)$ and the Bayes factor against the null hypothesis, with this assumption, is denoted by $F(k)$. A conjecture made in 1965 is almost…

指数模型后验分布的渐近正态性AI 解读

Let $f(x)$ be a $\operatorname{pdf}$ of exponential form with respect to the measure $\mu$. Suppose a prior $\operatorname{pdf}$ $\pi$ has been placed on the natural parameter space $\Omega$, where $\pi$ is a density (with respect to $m$-dimensional Lebesgue measure) which is both positive and continuous at $\tau^\ast$, the true but unknown parameter value. Using basic properties of exponential families and certain associated convex functions, it is shown that the posterior…

经验贝叶斯估计问题的收敛速度：连续情形AI 解读

In this paper we construct sequences of estimators for a density function and its derivatives, which are not assumed to be uniformly bounded, using classes of kernel functions. Utilizing these estimators, a sequence of empirical Bayes estimators is proposed. It is found that this sequence is asymptotically optimal in the sense of Robbins (Ann. Math. Statist. 35 (1964) 1-20). The rates of convergence of the Bayes risks associated with the proposed empirical Bayes estimators…

检测均值变化的检验AI 解读

Procedures are considered for testing whether the means of each variable in a sequence of independent random variables can be taken to be the same, against alternatives that a shift might have occurred after some point $r$. Bayesian test statistics as well as some statistics depending on estimates of $r$ are presented and their powers compared. Exact and asymptotic distribution functions are derived for some of the Bayesian statistics.

随机终止泊松过程的经验贝叶斯推断札记AI 解读

A Poisson process of events is considered which terminates after a random time. Termination is not direotly observable but has to be inferred from the nonoccurrence of events. The analysis of data from such processes is considered with particular emphasis on empirical Bayes methods, it being supposed that data on many similar processes are available. An application to inventory control is outlined.

部分贝叶斯推断与线性模型札记AI 解读

Some results are outlined for estimation in a replicated linear model in which the variance changes from cell to cell in accordance with an inverse gamma prior density. The primary parameters of the linear model are, however, treated as fixed unknown parameters. The analysis thus exemplifies the treatment of problems in which the nuisance parameters have a prior distribution but the parameters of primary interest do not.

允许误差方差变化的经验贝叶斯估计量AI 解读

For certain repetitive experiments where the parameters of interest vary randomly from experiment to experiment, improved estimators for the present values of the parameters can be obtained using the information from estimates in previous experiments. Martz & Krutchkoff (1969) provided empirical Bayes estimators for a multiple regression model with fixed error variance. Their resulte are extended to include the case in which the error variance is unknown and may vary from…

多项式回归模型不充分性的贝叶斯方法AI 解读

A method is presented which, in many cases, appears to be an improvement over the standard approach to the polynomial regression problem. This improvement is achieved by focusing attention on the deviation of the polynomial representation from the true underlying function. By fully utilizing the nature of this deviation, a model is constructed in which its properties are represented in terms of a Bayesian prior distribution. The model is analyzed to give parameter estimates…

用于估计火警真实性概率的经验贝叶斯方法AI 解读

An empirical Bayes approach is used to derive a Stein-type estimator of a multivariate normal mean when the components have unequal variances. This estimator is applied to estimating the probability that a fire alarm reported from a particular street box signals a structural fire rather than a false alarm or other emergency. The approach is to group alarm boxes into relatively homogeneous neighborhoods and to make empirical Bayes estimates of the “probability structural” for…

摘要暂缺

摘要暂缺

概率密度的启发式估计AI 解读

A heuristic procedure related to hypothesis testing is offered as a practical alternative to Bayesian estimation of probability densities. Although closely related to the ‘window’ method, it overcomes some of the problems associated with that technique. The proposed method is computationally rapid and easy to use.

摘要暂缺

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.

Lehmann 备择下两样本问题的贝叶斯分析AI 解读

A Bayesian analysis of the two-sample problem under the Lehmann alternatives is considered. This analysis is based on the rank order statistic. Comparisons are made with Savage's rank test.

狄利克雷过程的混合及其贝叶斯非参数应用AI 解读

A random process called the Dirichlet process whose sample functions are almost surely probability measures has been proposed by Ferguson as an approach to analyzing nonparametric problems from a Bayesian viewpoint. An important result obtained by Ferguson in this approach is that if observations are made on a random variable whose distribution is a random sample function of a Dirichlet process, then the conditional distribution of the random measure can be easily…

贝叶斯与非贝叶斯检验的折中：多项分布情形AI 解读

Compromises between Bayesian and non-Bayesian significance testing are exemplified by examining distributions of criteria for multinominal equiprobability. They include Pearson's X2, the likelihood-ratio, the Bayes factor F, and a statistic G that previously arose from a Bayesian model by “Type II Maximum Likelihood.” Its asymptotic distribution, implied by the theory of the “Type II Likelihood Ratio,” is remarkably accurate into the extreme tail. F too can be treated as a…

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