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On multivariate quantiles under partial orders

偏序下的多元分位数

This paper focuses on generalizing quantiles from the ordering point of view. We propose the concept of partial quantiles, which are based on a given partial order. We establish that partial quantiles are equivariant under order-preserving transformations of the data, robust to outliers, characterize the probability distribution if the partial order is sufficiently rich, generalize the concept of efficient frontier, and can measure dispersion from the partial order…

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Data Base Error Trapping and Prediction

数据库错误检测与预测

We develop and analyze models for a class of problems involving inferences about uncertain numbers of errors in data bases. In particular, we study two error detection methods. In the duplicate performance method, all items in a data base are processed by two individuals (or machines), and the resulting records are compared to find disagreements, which are then resolved. In the known errors method, a data base is first extended to include additional items known to be in…

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Data Base Error Trapping and Prediction

数据库错误检测与预测

We develop and analyze models for a class of problems involving inferences about uncertain numbers of errors in data bases. In particular, we study two error detection methods. In the duplicate performance method, all items in a data base are processed by two individuals (or machines), and the resulting records are compared to find disagreements, which are then resolved. In the known errors method, a data base is first extended to include additional items known to be in…

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Comment

the value of a that gave the smallest average value of the Brier score within the sample of 21 observations. The result was a = .01, which implies little or no serial dependence in the data. To further check the lack of serial dependence I performed a runs test on all 52 observations (probably a good thing to do first). The (approximate) standard normal test statistic was .2, confirming that the data were approximately serially independent. I then calculated successive…

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Combining Economic Forecasts

经济预测的组合

A method for combining forecasts may or may not account for dependence and differing precision among forecasts. In this article we test a variety of such methods in the context of combining forecasts of GNP from four major econometric models. The methods include one in which forecasting errors are jointly normally distributed and several variants of this model as well as some simpler procedures and a Bayesian approach with a prior distribution based on exchangeability of…

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A Decision-Theoretic Approach to Interval Estimation

区间估计的决策论方法

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.

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Probabilistic Prediction: Some Experimental Results

概率预测:若干实验结果

This article concerns a study in which personal probability assessments regarding the outcomes of football games were obtained. The results reported here, which include a detailed investigation of the assessments, an evaluation of the assessments in an inferential context and in a decision-theoretic context, and a discussion of the performance of a consensus, show that methods such as scoring rules and bets are useful in leading individuals to make careful probability…

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The Assessment of Prior Distributions in Bayesian Analysis

贝叶斯分析中先验分布的评估

In the Bayesian framework, quantified judgments about uncertainty are an indispensable input to methods of statistical inference and decision. Ultimately, all components of the formal mathematical models underlying inferential procedures represent quantified judgments. In this study, the focus is on just one component, the prior distribution, and on some of the problems of assessment that arise when a person tries to express prior distributions in quantitative form. The…

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