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成对比较实验的贝叶斯方法AI 解读

A Bayesian approach to the analysis of paired comparison experiments is presented. Two statistical models are considered: the multibinomial and the Bradley-Terry model. For each, the natural conjugate family of priors is used to represent prior beliefs, and the parameters of the prior are given meaningful interpretations. Two different estimators are suggested for the model parameters, the preference probabilities of the multibinomial model and the worth parameters of the…

凸二次回归曲线的贝叶斯估计AI 解读

The estimation of a quadratic regression curve when the quadratic coefficient is known to be positive is treated by a Bayesian method. The method extends easily to deal with a general linear model under parameter constraints.

直方图的贝叶斯估计方法AI 解读

This paper describes a Bayesian procedure for the simultaneous estimation of the probabilities in a histogram. A two-stage prior distribution is constructed which assumes that probabilities corresponding to adjacent intervals are likely to be closely related. The method employs multivariate logit transformations, and a covariance structure similar to that assumed in the first-order autoregressive process. Posterior estimates are obtained which combine information between the…

泊松过程发生率的贝叶斯序贯估计AI 解读

This paper provides numerical and analytical solutions to the problem of estimating the rate of a Poisson process. Optimal designs are obtained for various loss functions and the method of analysis is valid for any other loss function. The cost of sampling plays a fundamental role and since there are many practical situations where there is a time cost and an event cost, a sampling cost per observed event and a cost per unit time are both included.

有序多项数据的上下概率推断AI 解读

Dempster's method of upper and lower probabilities represents an attempt to obtain posterior probability statements about parameters without the necessity to incorporate prior information. We apply Dempster's method to the case of multinomial data for which there is some natural ordering of the categories. Inferences are derived for the sum of an arbitrary set of categories, the ratio of two such sums, and linear combinations of the category probabilities. Numerical examples…

数据编辑中识别错误的概率模型AI 解读

Certain data screening systems incorporate large numbers of logical checks on data entering the system. When violated, these logical checks indicate that various combinations of variates are in error. This article provides a model for assigning a probability measure to identify variates in error when there is a simultaneous violation of a set of logical checks. For certain symmetry conditions, the measure is a reasonable approximation to the posterior probability that given…

摘要暂缺

有序多项数据的概率上界与下界推断AI 解读

Dempster's method of upper and lower probabilities represents an attempt to obtain posterior probability statements about parameters without the necessity to incorporate prior information. We apply Dempster's method to the case of multinomial data for which there is some natural ordering of the categories. Inferences are derived for the sum of an arbitrary set of categories, the ratio of two such sums, and linear combinations of the category probabilities. Numerical examples…

数据编辑中识别错误的概率模型AI 解读

Certain data screening systems incorporate large numbers of logical checks on data entering the system. When violated, these logical checks indicate that various combinations of variates are in error. This article provides a model for assigning a probability measure to identify variates in error when there is a simultaneous violation of a set of logical checks. For certain symmetry conditions, the measure is a reasonable approximation to the posterior probability that given…

二项数据的贝叶斯方法AI 解读

A Bayesian procedure is obtained for the simultaneous estimation of the parameters of m binomial distributions. The method uses logistic transformations for the parameters and an exchangeable prior distribution. Information is combined between the binomial distributions to obtain estimates which, under certain circumstances, will be superior to the usual proportions. This paper is intended as a forerunner to a more general theory for the analysis of nonlinear models.

正态情形下后验均值的收缩AI 解读

Bayes estimation with a normal conditional distribution and an unknown prior distribution is considered. It is shown that the posterior mean always shrinks the observation toward a local maximum of the marginal distribution of the observation. For any symmetric, unimodal prior distribution itis shown that the posterior mean lies between the observation and the prior mean.

两种终端决策与多阶段抽样的贝叶斯决策规则渐近性质：第二部分AI 解读

Summary The paper is a continuation of a paper by the same authors. The model is based on a differentiable prior distribution, a linear loss function, an asymptotically normal sampling distribution and sampling costs proportional to the sample size. Asymptotic expressions are derived for sample sizes, acceptance and rejection criteria and the minimum regret for some k-stage sampling and decision procedures. In the present paper three cases not considered in the previous…

底层分布的选择与自适应估计AI 解读

In our approach to adaptive inference, selection of the true underlying family of distributions is needed. A Bayesian selection rule, which is based on non-informative priors for the parameters, and a multiple decision solution, that maximizes the weighted sum of the probabilities of correct selection, are presented; both of these yield a decision rule of the same form. A modified maximum likelihood solution is also given and is used to construct an adaptive estimate of the…

一种非参数经验贝叶斯估计量AI 解读

An empirical Bayes procedure introduced by Lemon & Krutchkoff (1969) is generalized to eliminate the need for knowledge of the conditional distribution. The procedure is then discussed from a non-Bayesian point of view.

常规统计问题中非正规先验贝叶斯推断的非贝叶斯后果AI 解读

For two routine statistical problems, inference about the ratio of two exponential means and inference about the coefficient of variation of a normal random variable, a serious pathology of Bayesian inference based on improper priors is uncovered and investigated.

一种连续经验贝叶斯平滑技术AI 解读

Maritz (1966) and Lemon & Krutchkoff (1969) each describe discrete empirical Bayes smoothing techniques. These techniques essentially attempt to approximate the prior distribution function. Here a continuous smoothing technique which is based on a smooth and continuous approximation to the prior density function is presented. Results from a Monte Carlo study of the Poisson distribution are reported which show that the continuous smoothing technique has desirable small-sample…

经验贝叶斯方法与标准治疗的重复使用AI 解读

The fact that more is generally known about a standard treatment in a clinical trial than about the test treatment is exploited in empirical Bayes estimates based on the results of using the same standard in other trials. Such estimates are proposed for the case of dicho-tomous response, and discussed in terms of an example in cancer research.

摘要暂缺

不完整数据下两样本问题的贝叶斯分析AI 解读

Suppose a sample of n units from a population with failure time cdf F(x) is put on test and the ith unit is removed from testing at min (xi, τi) where xi is the failure time of this unit and τi is a fixed truncation time. Similarly, let a second sample of units from be tested for times . A Bayesian approach for testing the hypothesis against the alternative based on such samples is considered. The posterior probability that (where k and the t's are defined later) is obtained.

不完整数据下两样本问题的贝叶斯分析AI 解读

Suppose a sample of n units from a population with failure time cdf F(x) is put on test and the ith unit is removed from testing at min (xi, τi) where xi is the failure time of this unit and τi is a fixed truncation time. Similarly, let a second sample of units from be tested for times . A Bayesian approach for testing the hypothesis against the alternative based on such samples is considered. The posterior probability that (where k and the t's are defined later) is obtained.

有限总体规模的序贯估计AI 解读

The problem of estimating the size of a finite population using sequential sampling is placed in a Bayesian framework, and an approximate numerical solution is obtained by the technique of truncated dynamic programming. The optimal stopping boundaries are compared with those discussed by Samuel.

有限总体规模的序贯估计AI 解读

The problem of estimating the size of a finite population using sequential sampling is placed in a Bayesian framework, and an approximate numerical solution is obtained by the technique of truncated dynamic programming. The optimal stopping boundaries are compared with those discussed by Samuel.

限制贝叶斯与经验贝叶斯估计量的风险：第二部分，经验贝叶斯情形AI 解读

We discuss compromises between Stein's estimator and the MLE which limit the risk to individual components of the estimation problem while sacrificing only a small fraction of the savings in total squared error loss given by Stein's rule. The compromise estimators “limit translation” away from the MLE. The calculations are pursued in an empirical Bayesian manner by considering their performance against an entire family of prior distributions on the unknown parameters.

区间估计的决策论方法AI 解读

Under an appropriate loss function, interval estimation may be regarded as a Bayesian decision-making procedure in which the objective is to find an interval that minimizes expected loss. For various loss functions, the behavior of the optimal interval is investigated, a comparison is made with the usual non-decision-theoretic interval estimates, and applications and examples are discussed.