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估计泊松过程到达率的贝叶斯序贯程序AI 解读

Let Wn, n = 0, 1, …, be the time until the nth arrival of a Poisson process with rate θ. Using loss L (θ, ) = θ−2(θ − )2 and sampling costs involving cost per arrival and cost per unit time, the Bayes sequential procedure is derived. The large-sample properties of the procedure are then studied in the classical framework, and the optimal stopping time N* is shown to be asymptotically equivalent to n*, that function of θ which minimizes the expected total cost given θ.…

估计泊松过程到达率的贝叶斯序贯程序AI 解读

Let Wn, n = 0, 1, …, be the time until the nth arrival of a Poisson process with rate θ. Using loss L (θ, ) = θ−2(θ − )2 and sampling costs involving cost per arrival and cost per unit time, the Bayes sequential procedure is derived. The large-sample properties of the procedure are then studied in the classical framework, and the optimal stopping time N* is shown to be asymptotically equivalent to n*, that function of θ which minimizes the expected total cost given θ.…

选择包含最优正态总体的子集的新程序AI 解读

A new procedure, called the fiducial procedure, is defined for selecting a subset of a collection of normal populations with common known variance. In the presence of an “indifference zone,” this procedure has probability at least P* of selecting the “best” population. An upper bound is obtained for the smallest indifference zone d* that satisfies the P* condition. Comparisons of relative merit are made between the fiducial procedure, Gupta's (1965) procedure, and an…

线性不等式约束下线性模型的贝叶斯分析AI 解读

This article considers the general linear model when the parameter space is subject to linear inequality constraints. A Bayesian analysis of this model is presented using a natural conjugate prior of the mixed type. Expressions are given for the probability that constraints are binding and for the distribution of the parameters. When prior information about the parameters is vague, the Bayesian and sampling methods of model selection are compared. The techniques are applied…

尼罗河问题：变点问题的条件解AI 解读

Inference is considered for the point in a sequence of random variables at which the probability distribution changes. An approximation to the conditional distribution of the maximum likelihood estimator of the changepoint given the ancillary values of observations adjacent to the estimated changepoint is derived and shown to be numerically equal to a Bayesian posterior distribution for the changepoint. A hydrological example is given to show that inferences based on the…

非正常先验、样条平滑与回归模型误差防范AI 解读

Summary Spline and generalized spline smoothing is shown to be equivalent to Bayesian estimation with a partially improper prior. This result supports the idea that spline smoothing is a natural solution to the regression problem when one is given a set of regression functions but one also wants to hedge against the possibility that the true model is not exactly in the span of the given regression functions. A natural measure of the deviation of the true model from the span…

逆高斯分布及其统计应用综述AI 解读

Summary This paper reviews the development of the inverse Gaussian distribution and of statistical methods based upon it from the paper of Schrödinger (1915) to the present (1978). After summarizing the properties of the distribution, the paper presents tests of hypotheses, estimation, confidence intervals, regression and “analysis of variance” based upon the inverse Gaussian. its potential role in reliability work is discussed and work on Bayesian statistics is reviewed…

渐近最优估计的可容许表示AI 解读

A sequence of medians of posterior distributions is approximately median unbiased of order $o(n^{-1}) \operatorname{iff}$ the prior density is equal to the square root of Fisher's information function. It is shown that in this case the sequence of medians of posterior distributions is even an optimum sequence of estimates within the class of all estimator sequences being approximately median unbiased of order $o(n^{-1}).$ The result is proved by showing equivalence with an…

经验贝叶斯平方误差损失估计问题的解法AI 解读

Asymptotically optimal empirical Bayes squared error loss estimation procedures are developed for three families of continuous distributions, uniform $(0, \theta), \theta > 0,$ uniform $\lbrack \theta, \theta + 1), \theta$ arbitrary, and a location parameter family of gamma distributions. The approach taken is to estimate the Bayes estimator directly. However, for the $\lbrack \theta, \theta + 1)$ case, it is shown that the indirect approach of applying the Bayes estimator,…

序贯检验的渐近效率（二）AI 解读

An asymptotic expression is given for the $\log$ error probability of a sequential test based on a random walk. This may be used to compute limiting relative efficiencies of such tests. The results are illustrated for the one-sided normal testing problem with an asymptotic Bayes test due to Schwarz. Some numerical comparisons are given for five sequential tests of a normal mean.

多元问题中的广义贝叶斯估计量AI 解读

Several problems involving multivariate generalized Bayes estimators are investigated. First, a characterization of admissible estimators as generalized Bayes estimators is developed for certain multivariate exponential families and quadratic loss. The problem of verifying whether or not an estimator is generalized Bayes is also considered. Next, an important class of estimators for a multivariate normal mean is considered. (The class includes many minimax, empirical Bayes,…

基于删失样本的贝叶斯非参数生存曲线估计量的大样本理论AI 解读

Let $X_1, \cdots, X_n$ be i.i.d. $F_0$ and let $Y_1, \cdots, Y_n$ be independent (and independent also of $X_1, \cdots, X_n$) random variables. Then assuming that $F$ is distributed according to a Dirichlet process with parameter $\alpha,$ the authors obtained the Bayes estimator $\hat{F}_\alpha$ of $F$ under the loss function $L(F, \hat{F}) = \int (F(u) - \hat{F}(u))^2 dw(u)$ when $X_1, \cdots, X_n$ are censored on the right by $Y_1, \cdots, Y_n,$ respectively, and when it…

右删失观测下分布与生存函数的经验贝叶斯估计AI 解读

This paper provides an empirical Bayes approach to the problem of nonparametric estimation of a distribution (or survival) function when the observations are censored on the right. The results use the notion of a Dirichlet process prior introduced by Ferguson. The paper presents a generalization to the case of right censored observations of the rate result of an empirical Bayes nonparametric estimator of a distribution function of Korwar and Hollander in the uncensored case.…

截断参数的序贯估计AI 解读

Consider the problem of sequentially estimating the parameter θ of a uniform distribution on (0, θ). It is shown that if the loss is measured by squared error plus a linear cost function, and the prior on θ is given by a Pareto distribution, a simple heuristic procedure incurs an excess risk above the Bayes risk not greater than the cost of three observations. The result is extended to a wider class of distributions which includes the uniform and to a wide class of priors.

回归中的季节性：平滑先验的应用AI 解读

This article argues that conventional approaches to the treatment of seasonality in econometric investigation are often inappropriate. A more appropriate technique is to allow all regression coefficients to vary with the season, but to constrain them to do so in a smooth fashion. A Bayesian method of estimating smoothly varying seasonal coefficients is developed, based on Shiller's (1973) approach to estimating distributed lags. In a sampling experiment, this technique…

存在无应答时回归分析的样本量选择AI 解读

Assuming nonresponse, inference concerning the regression coefficients of a multiple linear regression is considered from a Bayesian viewpoint. We exploit a two-phase sampling scheme. At each phase the sample design is of the following type: Select a random sample of size n with n 1 responses obtained. Then, a subsample of size n 2(0 ≤ n 2 ≤ n — n 1) is selected from the n — n 1 nonrespondents. Assuming 100 percent response from the units in the subsample, the principal…

回归中的季节性：平滑先验的应用AI 解读

This article argues that conventional approaches to the treatment of seasonality in econometric investigation are often inappropriate. A more appropriate technique is to allow all regression coefficients to vary with the season, but to constrain them to do so in a smooth fashion. A Bayesian method of estimating smoothly varying seasonal coefficients is developed, based on Shiller's (1973) approach to estimating distributed lags. In a sampling experiment, this technique…

截断参数的序贯估计AI 解读

Consider the problem of sequentially estimating the parameter θ of a uniform distribution on (0, θ). It is shown that if the loss is measured by squared error plus a linear cost function, and the prior on θ is given by a Pareto distribution, a simple heuristic procedure incurs an excess risk above the Bayes risk not greater than the cost of three observations. The result is extended to a wider class of distributions which includes the uniform and to a wide class of priors.

存在无应答时回归分析的样本量选择AI 解读

Assuming nonresponse, inference concerning the regression coefficients of a multiple linear regression is considered from a Bayesian viewpoint. We exploit a two-phase sampling scheme. At each phase the sample design is of the following type: Select a random sample of size n with n 1 responses obtained. Then, a subsample of size n 2(0 ≤ n 2 ≤ n — n 1) is selected from the n — n 1 nonrespondents. Assuming 100 percent response from the units in the subsample, the principal…

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分布函数的贝叶斯置信带AI 解读

A set of recurrences is developed for computing the probability content of any prior or posterior confidence bands for a distribution function assuming the parameter of the prior Dirichlet process known. When the prior parameter is unknown and is estimated from the sample, nonparametric estimates of the probability content of the posterior bands are obtained.

分类问题的渐近有效解AI 解读

We study a class of decision rules based on an adaptive partitioning of an Euclidean observation space. The class of partitions has a computationally attractive form, and the related decision rule is invariant under strictly monotone transformations of coordinate axes. We provide sufficient conditions that a sequence of decision rules be asymptotically Bayes risk efficient as sample size increases. The sufficient conditions involve no regularity assumptions on the underlying…

用于选择回归模型的后验概率AI 解读

A simple Bayesian formula for the posterior probability of one of several regression models is shown to be systematically misleading unless all models have the same number of parameters. Even in this case the use of improper priors leads to arbitrary inferences, as it does more generally. An alternative weighting for choosing a model is suggested and the relationship between significance tests and data-dependent priors mentioned.

摘要暂缺