日期精度：到日 2009 篇 · 到月 2034 篇 · 到年 253 篇 · 未提供 1 篇
一种经验贝叶斯平滑技术
Empirical Bayes procedures generally require the estimation of marginal probabilities. Maritz (1996) showed that the usual estimator for a discrete probability smoothing the estimators of discrete probabilities. Here we present a general procedure for smoothing probabilities and apply it to the Poisson situation.
泊松分布的经验贝叶斯估计
SUMMARY A number of established methods of empirical Bayes estimation for the Poisson distribution are surveyed, and their performances are compared. A new method of smooth empirical Bayes estimation is presented, and its performance is also studied. The question of assessing the effectiveness of the empirical Bayes approach in practice is examined.
点估计中的若干经验贝叶斯技术
In point estimation with a squared-error loss function the Bayes estimator is the posterior mean. In the empirical Bayes approach we must construct a consistent sequence of estimators for this posterior mean using past experience. This construction is done here for four general families of conditional distributions which include as special cases: the Poisson, the gamma, the normal and the uniform.
特征根与特征向量的贝叶斯估计：以二元正态分布为重点
This paper discusses from a Bayesian viewpoint some aspects of the estimation of latent roots and vectors of the covariance matrix of the bivariate normal distribution. The joint distribution of (i) the angle of the canonical transformation, and (ii) the ratio of the larger root to the total variance is considered in detail and illustrated by an example. Also discussed is the problem of making inferences about the larger roots, and several simple approximations to the…
经验贝叶斯估计量的 ε 渐近最优性
Robbins (1964) gives conditions under which empirical Beyes estimators are asymptotically optimal. The conditions require the loss function to be bounded in the parameter. This does not hold in some important situations including the squared error loss. Here we give weaker conditions and prove a weaker result, ε asymptotic optimality, which is equivalent to asymptotic optimality in practical situations.
转移概率的极大似然与贝叶斯估计
In this paper, maximum likelihood and Bayesian methods are presented for estimating transition probabilities when data in the form of aggregated proportions are available. The probability function for the observed proportions is assumed to have a multinomial distribution under the Lexis scheme. The multivariate beta distribution is used as the prior probability density function in formulating the Bayesian estimator. The results of some Monte Carlo experiments provide some…
利用先验信息进行分层与多阶段抽样的最优分配
The author [1], [2] has given an algorithm for finding that stratified allocation which minimizes the posterior variance of the overall population mean subject to a budget constraint under a model in which a normal prior distribution and independent normal sampling distributions were assumed. The budget constraint assumed a variable per unit cost of observation. In the present paper these results are extended to cover the case where there are fixed costs, as well as variable…
连续先验下的混合二项分布与概率参数的后验分布
Summary Asymptotic expansions are derived for the mixed binomial distribution and the posterior distribution of p for a continuous prior distribution. Expansions are also found for the first four moments of the posterior distribution. Applications to estimation and sampling inspection are discussed.
贝叶斯推断的一种推广
Summary Procedures of statistical inference are described which generalize Bayesian inference in specific ways. Probability is used in such a way that in general only bounds may be placed on the probabilities of given events, and probability systems of this kind are suggested both for sample information and for prior information. These systems are then combined using a specified rule. Illustrations are given for inferences about trinomial probabilities, and for inferences…
Haavelmo 模型的贝叶斯分析
In this paper, the exact posterior distributions of the parameters of Haavelmo's model I is derived for locally uniform prior distributions. Marginal distributions of the parameters have been obtained for Haavelmo's data. Then the predictive probability density of the model is derived for given values of the exogenous variable, investment. In order to check some of the specifying assumptions, the model is expanded and analyzed under the assumption that the error terms are…
百分位数的后验分布：有限总体抽样中的贝叶斯推断
A Bayesian approach to inference about the percentiles and other characteristics of a finite population is proposed. The approach does not depend upon, though it need not exclude, the use of parametric models.Some related questions concerning the existence of exchangeable distributions are considered. It is shown that there are no countably additive exchangeable distributions on the space of observations which give ties probability 0 and for which a next observation is…
单向随机效应模型中均值的贝叶斯估计
The problem of estimating the means in the one-way random effect model yjk = θj+ejk is considered from a Bayesian viewpoint. Posterior distributions of the θj are obtained under the assumption that the θj are independently drawn from a Normal population N(θ, σ22) and that the ejk are independent random errors having a N(0, σ21) distribution. It is shown that the posterior distributions of the θj are clustered more closely together than are the corresponding distributions for…
若干异常值问题的贝叶斯方法
The problem of outlying observations is considered from a Bayesian viewpoint. We suppose that each of the observations in an experiment in an experiment may come from either a ‘good’ run or a ‘bad’ run. By specifying the models corresponding to good and bad runs and the prior probabilities of which runs being bad, we then employ standard Bayesian inference procedures to derive the appropriate analysis. In particular, we consider the linear model and assume that a good…
线性函数关系的贝叶斯估计
Summary The purpose of this note is twofold. First, to demonstrate by means of an example that a statistical approach based solely on the likelihood function can be misleading, whereas the Bayesian method yields sensible results. Second, to develop the Bayesian method and apply the results to the problem of estimating a linear functional relationship. In Section 1 we discuss the likelihood approach. Section 2 concerns the Bayesian method, which is applied to the functional…
多元回归中的变量选择
Summary This paper is concerned with the analysis of data from a multiple regression of a single variable, y, on a set of independent variables, x 1,x 2,...,xr. It is argued that the form of the analysis should depend on the use that is to be made of the regression, and that therefore an approach employing ideas from decision theory may be worth while. Two situations are analysed in this way: in the first it is desired to predict a future value of y; in the second we wish to…
抽样调查的一种新估计理论
A new estimation theory for sample surveys is proposed, the basic feature of which is a special parametrization of finite populations based on the assumptions that a character attached to the units is measured on a known scale with a finite set of scale points. In the class of estimators which do not functionally depend on the identification labels preattached to the units, the following results are proved: (1) For simple or stratified simple random sampling without…
线性回归模型中经验贝叶斯估计量的使用
New estimators for the parameters in the linear regression model are presented, using not only the usual random sample of observations, but also past experience in the form of previous estimates of parameters in similar but independent situations. The regression parameters are considered to be random variables. Bayes estimators are given for a squared error loss function. Even though the prior density of the parameter is unknown, the Bayes estimator can be written in terms…
假设检验与复合决策问题的平滑经验贝叶斯方法
The smooth empirical Bayes approach is based on using past observations to estimate a specified type of approximation to the prior distribution. This approach is applied to problems of empirical Bayes hypothesis testing and to the compound decision problem. Problems involving composite hypotheses are considered which have, hitherto, received much less attention than the case of two simple hypotheses. The methods are shown to be asymptotically optimal and results of studies…
位置与尺度参数的线性损失区间估计
Estimation, in both theory and practice, tends to be divided into two almost distinct branches. On the one hand, point estimation, by providing a working value for the unknown true parameter value, is undoubtedly useful in further investigations of the given situation although its reliability may be difficult to assess in real terms through the medium of the estimated standard error. On the other hand, confidence interval estimation, by presenting a whole set of more or less…
双随机成分线性模型的贝叶斯分析：平衡不完全区组设计
Abstract : The paper considers linear models which contain two random components and enable representation of general designs with block effects random. It shows how, within a Bayesian framework, to combine the intra- and inter-block information about the location parameters. The balanced incomplete block design, an important special case, is considered in detail and illustrated by an example. A simple approximation to the marginal distribution of an individual contrast is…
若干异常值问题的贝叶斯处理
The problem of outlying observations is considered from a Bayesian viewpoint. We suppose that each of the observations in an experiment in an experiment may come from either a ‘good’ run or a ‘bad’ run. By specifying the models corresponding to good and bad runs and the prior probabilities of which runs being bad, we then employ standard Bayesian inference procedures to derive the appropriate analysis. In particular, we consider the linear model and assume that a good…