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贝叶斯线性运动学与贝叶斯线性—贝叶斯图模型AI 解读

Probability kinematics (Jeffrey, 1965, 1983) furnishes a method for revising a prior probability specification based upon new probabilities over a partition. We develop a corresponding Bayes linear kinematic for a Bayes linear analysis given information which changes our beliefs about a random vector in some generalised way. We derive necessary and sufficient conditions for commutativity of successive Bayes linear kinematics which depend upon the eigenstructure of the joint…

贝叶斯线性充分性与专家后验评估系统AI 解读

SUMMARY Data arising in the form of expert assessments are received by a decision maker. The decision maker is required to estimate a set of unknown quantities, and receives expert assessments at varying levels of accuracy, on samples of the quantities of interest. We present a Bayes linear analysis of this problem. In the absence of other assessments, the decision maker will accept as his or her current estimate of any single quantity the most accurate received assessment…

一个似然悖论AI 解读

SUMMARY The Fraser–Monette–Ng example, strengthened by Joshi, is simplified and further strengthened. The claim by Joshi that it gives a counter-example to the likelihood principle, and that this counter-example also covers the case of a finite parameter space, is disputed.

回归问题的贝叶斯分析AI 解读

A general Bayesian formulation of the regression problem is considered, which derives from a direct specification of a prior distribution for the unknown joint probability distribution of the random variables. The resulting estimators are related to the least squares and ridge estimators of the regression coefficients.

回归问题的贝叶斯分析AI 解读

A general Bayesian formulation of the regression problem is considered, which derives from a direct specification of a prior distribution for the unknown joint probability distribution of the random variables. The resulting estimators are related to the least squares and ridge estimators of the regression coefficients.

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.

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.

若干非参数问题的近似贝叶斯解AI 解读

The problem of making inferences about real functions of a probability distribution of unknown form is examined in a Bayesian nonparameteric framework. With respect to a general quadratic loss function, Bayes estimates within the class of linear combinations of a given set of functions on the sample space are obtained for general functions on the distribution space. The result is then used to derive Bayes polynomial estimates of the moments of the distribution.

摘要暂缺

回归分析中的岭型估计量AI 解读

Summary An examination of the mean-square error properties of a class of shrinkage estimators for the normal regression model leads to a new derivation of the Hoerl–Kennard (1970) Ridge estimator and its generalization. Comparison is made with the James–Stein estimator, and with the generalized-inverse estimator proposed by Marquardt (1970). A Bayesian approach is noted.

An approximate method is suggested for evaluating the decision rules of Watson (1974) for situations where only a partial specification of the prior distribution can be given. The method is applied to the problem of estimating the mean of a distribution of unknown form, under quadratic loss.