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指数失效模型下的总体规模估计AI 解读

We are given J observations obtained by truncated sampling of a population of N items which fail independently according to the exponential distribution, where both N and the scale parameter of the exponential are unknown. Estimates of N are developed, and compared. These are conditional and unconditional maximum likelihood estimates, and a class of Bayes modal estimates. On the basis of second-order asymptotic properties, one of the Bayes estimates is singled out as most…

有限泊松过程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的一则札记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.

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惩罚函数法下概率密度的非参数最大似然估计AI 解读

Tne maximum likelihood estimate of a probability density function based on a random sample does not exist in the nonparametric case. For this reason and others based on heuristic Bayesian considerations Good and Gaskins suggested adding a penalty term to the likelihood. They proposed two penalty terms; however they did not establish existence or uniqueness of their maximum penalized likelihood estimates. Good and Gaskins also suggested an alternate approach for calculating…

二维列联表的贝叶斯估计方法AI 解读

Summary Estimation methods are proposed for the row, column and interaction effects in two-way contingency tables, the one-way table being treated as a special case. The methods are appropriate when the parameters are thought a priori to be related to each other. The posterior estimates have the practical effects of smoothing the contingency table, and are valid even if some of the cell frequencies are zero. The main case treated is where particular assumptions of…

分布尾部推断的一种简单通用方法AI 解读

A simple general approach to inference about the tail behavior of a distribution is proposed. It is not required to assume any global form for the distribution function, but merely the form of behavior in the tail where it is desired to draw inference. Results are particularly simple for distributions of the Zipf type, i.e., where $G(y) = 1 - Cy^{-\alpha}$ for large $y$. The methods of inference are based upon an evaluation of the conditional likelihood for the parameters…

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独立泊松总体均值的同时估计AI 解读

A procedure is derived for simultaneously estimating the means of Poisson populations using independent samples. The total loss is the sum of component, standardized squared error losses. The derived procedure is minimax, generalized Bayes, admissible relative to a large class, and better than using the sample means as estimators of the corresponding population means. The latter procedure is compared with the derived procedure, both numerically and asymptotically.

切换回归与随机系数回归模型的贝叶斯及非贝叶斯分析AI 解读

Quandt [20] analyzed the problem of discontinuous shifts in regression regimes at unknown points in the data series. We note that Quandt's statistical approach based solely on the likelihood function can be misleading, whereas the Bayesian method based on a proper prior distribution of the unknown parameters yields sensible results. However, the exact evaluation of the posterior distribution is unusually burdensome and cannot be simplified even in large samples. To avoid…

随机变量序列变点推断的贝叶斯方法AI 解读

A Bayesian approach is considered to the problem of making inferences about the point in a sequence of random variables at which the underlying distribution changes. Inferences are based on the posterior probabilities of the possible change-points. Detailed analyses are given for cases in which the distributions are binomial and normal, and numerical illustrations are provided. An informal sequential procedure is also noted.

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Summary An empirical Bayes estimator which can be constructed without explicit estimation of the prior distribution is called a simple empirical Bayes estimator. Construction of such estimators for a single unknown parameter of a general continuous distribution is considered. Examples are given and their performance is examined.

线性后验期望的唯一性关系AI 解读

Summary When the posterior expectation of the population mean is a linear function of the sample observation, then the moments of the prior distribution are uniquely determined. From this, a fairly general condition is given for establishing that the prior distribution for the population mean has a unique form.

自适应心理测验中二元响应的贝叶斯序贯程序AI 解读

This article is concerned with a generalization of the problem of estimation of median effective dose in bioassay with a normal quantal response curve. A new kind of Bayesian motivated procedure is introduced which leads to a strongly consistent estimator. The convergence is robust in that it holds for a bundle of sequences of design vectors—an important feature in a mental testing context where a specified design vector cannot be produced on demand.

给定检验强度下的最优双重抽样检验：正态分布AI 解读

For a normally distributed random variable with unknown mean θ and known variance, optimum double sampling tests of strength (θ1, α, θ2, β) are found and compared with the single sampling test and the SPRT of the same strength. Two optimality criteria are used—minimax ASN and Bayes ASN. Tables of these optimum tests are given. Approximations to optimum double sampling tests for Poisson and binomially distributed variables are discussed.

已知状态数量的切换回归模型：贝叶斯分析AI 解读

Some aspects of Bayesian methods of inference relative to switching regression models are analyzed. It is shown that Bayesian confidence intervals and tests may be obtained by using Student's t and χ2 distributions. Mean biases and MSE of some Bayesian estimates are compared by Monte Carlo methods with those of the ML estimate. The MSE of the Bayesian estimates were uniformly smaller than those of the ML estimate. An experiment designed by Quandt [11] is also analyzed.

使用 Stein 估计量及其推广进行数据分析AI 解读

In 1961, James and Stein exhibited an estimator of the mean of a multivariate normal distribution having uniformly lower mean squared error than the sample mean. This estimator is reviewed briefly in an empirical Bayes context. Stein's rule and its generalizations are then applied to predict baseball averages, to estimate toxomosis prevalence rates, and to estimate the exact size of Pearson's chi-square test with results from a computer simulation. In each of these examples,…

自适应心理测验中二元反应的贝叶斯序贯程序AI 解读

This article is concerned with a generalization of the problem of estimation of median effective dose in bioassay with a normal quantal response curve. A new kind of Bayesian motivated procedure is introduced which leads to a strongly consistent estimator. The convergence is robust in that it holds for a bundle of sequences of design vectors—an important feature in a mental testing context where a specified design vector cannot be produced on demand.

关于若干贝叶斯非参数估计的一则说明AI 解读

With respect to a general quadratic loss function, the Bayes rule for the mean of a probability distribution of unknown form is obtained, in the class of linear functions of the sample. The associated Bayes risk is also obtained. A number of recent results in the literature are shown to be direct corollaries of this result, and applications are given for the empirical distribution function of the sample.

已知前 N 阶矩时随机概率的极小极大估计AI 解读

$X$ and $\Theta$ are random variables; for given $\Theta = \theta$, the conditional distribution of $X$ is binomial with parameters $N$ and $\theta$; the first $N$ moments of $\Theta$ are known. An estimate of $\Theta$ is made based on the observed value of $X$, the risk being defined in terms of squared error loss. It is shown that as conjectured by H. Robbins, the ratio of the Bayes risk to the minimax risk for all possible distributions of $\Theta$ uniformly tends to…

以最小误分类概率为目标的线性特征选择AI 解读

We describe an approach to linear feature selection for $n$-dimensional normally distributed observation vectors which belong to one of $m$ populations. More specifically, we consider the problem of finding a rank $k k \times n$ matrix $B$ which minimizes the probability of misclassification with respect to the $k$-dimensional transformed density functions when a Bayes optimal (maximum likelihood) classification scheme is used. Theoretical results are presented which, for…

参数分解与基于显著性、似然及客观后验的推断AI 解读

The concepts of significance, likelihood, and objective posterior have wide ranges of application in statistics. For certain very simple applications--single location variable--there has been recognition that the three concepts produce equivalent numerical results, specifically the equality of observed level of significance, integrated likelihood extreme values, and integrated objective posterior extreme values. The most general model permitting the use of the three concepts…

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