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贝叶斯经验贝叶斯AI 解读

A Bayesian approach is given for various kinds of empirical Bayes problems. In particular it is shown that empirical Bayes procedures are really non-Bayesian, asymptotically optimal, classical procedures for mixtures. In some situations these procedures are Bayes with respect to some prior and in other situations, there is no prior for which they are Bayes. Several examples of these concepts are given as well as a general theory showing the difference between an empirical…

可交换性在统计推断中的作用AI 解读

This paper is concerned with basic problems of statistical inference. The thesis is in three parts: (1) that inference is a procedure whereby one passes from a population (or sample) to a new individual; (2) that this connection can be established using de Finetti's idea of exchangeability or Fisher's concept of a subpopulation; (3) in making the connection use must be made of the appropriate probability. These three principles are used in a variety of situations and the…

法庭科学中的一个统计问题AI 解读

SUMMARY The problem of deciding whether two sets of fragments have come from a common source frequently arises in forensic science. This paper provides a solution in the realistic case where the distribution is nonnormal. The normal case is also discussed because it is there easier to understand the nature of the solution and, in particular, its relationship to significance tests. The solution requires the distribution function of the product of standardized normal…

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线性函数关系的贝叶斯估计AI 解读

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AI 解读

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…

序贯抽样：二项与正态随机变量在线性损失下的两个决策问题AI 解读

D. V. LINDLEY, B. N. BARNETT; Sequential sampling: two decision problems with linear losses for binomial and normal random variables, Biometrika, Volume 52

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正态分布方差推断用表AI 解读

D. V. LINDLEY, D. A. EAST, P. A. HAMILTON; Tables for making inferences about the variance of a normal distribution, Biometrika, Volume 47, Issue 3-4, 1 De

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统计推断AI 解读

Summary The subject matter of mathematical statistics may be divided into two parts, the theory of probability and the theory of inference. The first is concerned with deductions from the population to the sample; the second with inferences from the sample to the population, and may further be subdivided into the design and analysis of experiments. In the present paper we are concerned with this latter subdivision. We use the axiomatic theory of Kolmogorov as our theory of…

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回归线与线性函数关系AI 解读

Abstract The first half of this paper solves the following problem : if there is a linear multiple regression between n variates, under what conditions will the regression continue to be linear when the variates are influenced by error? The new regression coefficients are obtained in terms of the original coefficients. This leads in the second half to a discussion of the use of regression lines and functional relationships in statistical methodology. In the case of normal…

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