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用于直方图平滑的滤波变量先验分布AI 解读

We develop prior distributions for histogram inference favoring smooth population frequencies; that is, probability vectors with small differences for neighboring categories. We give a theory of prior-random probability vectors representable as a linear transform, or “filter,” of a standard random probability vector, or equivalently, a random weighted average of nonrandom smooth probability vectors. Promising methods of prior assessment are given based on elicitation of a…

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回归变量选择问题中的先验分布 elicitationAI 解读

This paper addresses the problem of quantifying expert opinion about a normal linear regression model when there is uncertainty as to which independent variables should be included in the model. Opinion is modeled as a mixture of natural conjugate prior distributions with each distribution in the mixture corresponding to a different subset of the independent variables. It is shown that for certain values of the independent variables, the predictive distribution of the…

线性回归问题中专家意见的量化AI 解读

SUMMARY This paper describes a method for choosing a natural conjugate prior distribution for a normal linear sampling model. A person using the method to quantify his/her opinions performs specified elicitation tasks. The hyperparameters of the conjugate distribution are estimated from the elicited values. The method is designed to require elicitation tasks that people can perform competently and introduces a type of task not previously reported. A property of the method is…

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多重超几何函数的概率解释与统计用途AI 解读

This article reviews and interprets recent mathematics of special functions, with emphasis on integral representations of multiple hypergeometric functions. B.C. Carlson's centrally important parameterized functions R and ℛ, initially defined as Dirichlet averages, are expressed as probability-generating functions of mixed multinomial distributions. Various nested families generalizing the Dirichlet distributions are developed for Bayesian inference in multinomial sampling…

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基于选择性报告数据的似然与贝叶斯推断AI 解读

If the reported data of an experiment have been subject to selection, then inference from such data should be modified accordingly. We investigate the modification required to the face-value likelihood. In particular, we derive conditions under which no modification is necessary and the data can be taken at face value.

尾部概率能否近似贝叶斯因子？AI 解读

Inequalities are given relating the tail area for a nested sharp hypothesis to the Bayes factor based on the event of “significance” considered as data. This Bayes factor based on an insufficient statistic is, in turn, expressed as a weighted average of full-data Bayes factors. Lindley's “statistical paradox” is generalized and other comparisons made in the normal sampling context. A new Bayesian interpretation is given for the traditional two-tailed critical level. An…

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尾部概率能否作为贝叶斯因子的近似？AI 解读

Inequalities are given relating the tail area for a nested sharp hypothesis to the Bayes factor based on the event of “significance” considered as data. This Bayes factor based on an insufficient statistic is, in turn, expressed as a weighted average of full-data Bayes factors. Lindley's “statistical paradox” is generalized and other comparisons made in the normal sampling context. A new Bayesian interpretation is given for the traditional two-tailed critical level. An…

近似后验分布AI 解读

This paper proposes the use of approximate posterior distributions resulting from operational prior distributions chosen with regard to the realized likelihood function. L.J. Savage's “precise measurement” is generalized for approximation in terms of an arbitrary operational prior density, including mixed-type prior distributions with positive probabilities on singular subsets. A new approximation is also given relating such distributions to absolutely continuous…

评论：非可积先验在贝叶斯推断中的作用AI 解读

This illuminating paper by Stone is the latest in a series of papers drawing attention to possible disadvantages of using nonintegrable prior densities. In these comments, I shall attempt to clarify the role of nonintegrable prior densities in Bayesian inference, thereby providing also a delayed answer to James and Stein [5], Dempster [1], Stone [9], Klotz, et al. [6], and Portnoy [7]. More extensive discussion of the ideas introduced will be given in a subsequent paper.