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自然指数族的共轭参数化AI 解读

Recently, Consonni and Veronese have shown that the form of the standard conjugate distribution for the mean parameter μ of a univariate natural exponential family F coincides with that of the distribution induced on μ by the standard conjugate distribution for the canonical parameter if and only if F has a quadratic variance function. In this article we present significant extensions of this result, identifying conditions under which transformations of the canonical or mean…

不确定性的诸方面：献给 D. V. LindleyAI 解读

Dennis Lindley: The First 70 Years The Operational Bayesian Approach Pivotal Inference Illustrated on the Darwin Maize Data Bayes Theory in Latent Variable Modelling Bayesian Sampling Schemes for Auditors Optimal Prediction with Hierarchical Models: Bayesian Clustering Inference for a Covariance Matrix The Role of Statistical Theory in Decision Aiding The Signature as a Covariate in Reliability and Biometry Residual Analysis and Outliers in Hierarchical Models The Island…

更正：对效力曲线施加先验形状约束的非参数贝叶斯生物测定AI 解读

P. Ramgopal, P. W. Laud, A. F. M. Smith, Amendments and Corrections: Nonparametric Bayesian Bioassay with Prior Constraints on the Shape of the Potency Curve, Biometrika, Vol. 81, No. 3 (Aug., 1994), p. 631

涉及指数族的贝叶斯推断中后验累积量的关系AI 解读

For Bayesian inference in one-parameter contexts where either the likelihood or the prior has an exponential family form, relationships are derived for posterior moments and cumulants of (functions of) both the canonical and the expectation parameters. The identities exhibited generalize the simple relationships well known in the conjugate analysis case. Applications of these results are indicated in the areas of Bayesian robustness and approximation. In particular, results…

指数族贝叶斯推断中的后验累积量关系AI 解读

For Bayesian inference in one-parameter contexts where either the likelihood or the prior has an exponential family form, relationships are derived for posterior moments and cumulants of (functions of) both the canonical and the expectation parameters. The identities exhibited generalize the simple relationships well known in the conjugate analysis case. Applications of these results are indicated in the areas of Bayesian robustness and approximation. In particular, results…

近似非高斯贝叶斯估计与众数一致性AI 解读

SUMMARY A new recursive estimation procedure is proposed for the location of a dynamic linear model with non-normal errors. The procedure is a modification of a modal approximation algorithm, which is shown to be prone to instabilities. The modification is motivated by a notion of posterior modal consistency.

SUMMARY The use of the Gibbs sampler for Bayesian computation is reviewed and illustrated in the context of some canonical examples. Other Markov chain Monte Carlo simulation methods are also briefly described, and comments are made on the advantages of sample-based approaches for Bayesian inference summaries.

效力曲线形状受先验约束的非参数贝叶斯生物测定AI 解读

We consider the problem of implementing nonparametric Bayesian analysis of bioassay problems when the prior constrains the form of the potency curve (for example, to be convex, concave or ogive). Sampling based approaches to calculating posterior features of interest are detailed and illustrated. Extensions to prior constraints on hazard rates are outlined.

效力曲线形状先验约束下的非参数贝叶斯生物测定AI 解读

We consider the problem of implementing nonparametric Bayesian analysis of bioassay problems when the prior constrains the form of the potency curve (for example, to be convex, concave or ogive). Sampling based approaches to calculating posterior features of interest are detailed and illustrated. Extensions to prior constraints on hazard rates are outlined.

正态位置参数后验矩的精确与近似表达AI 解读

SUMMARY The forms of first and second posterior moments for a normal location parameter are identified for a rather general class of prior distributions. Exact and approximate illustrations are given where the prior distribution is double exponential or Student t respectively.

生物医学时间序列的建模与监测AI 解读

A framework for modeling and monitoring medical time series is developed, based on extensions to the linear dynamic model. The approach is designed to provide for on-line, recursive updating and inference for time series that are subject to several forms of potential discontinuous change, and that may have missing values. The models and methods introduced are illustrated with three biomedical series.

一个考古年代推断问题AI 解读

An archaeological dating problem is presented and analyzed. The analysis is based on a data-generating model, which takes careful account of the various kinds of uncertainty involved in relating observed radiocarbon dates of artifacts to successive chronological beginning and ending dates of significant archaeological phases. In addition to its intrinsic interest as a possible model for many kinds of archaeological data of this type, the model poses some challenging…

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有限混合分布的统计分析AI 解读

Statistical Problems. Applications of Finite Mixture Models. Mathematical Aspects of Mixtures. Learning About the Parameters of a Mixture. Learning About the Components of a Mixture. Sequential Problems and Procedures.

模糊先验信息下线性与对数线性模型的贝叶斯因子AI 解读

Summary The Bayes factor, or integrated likelihood ratio, provides a possible Bayesian alternative to the standard F ‐test procedure for comparing two linear models. However, if vague prior information for the model parameters is represented by limiting improper prior forms, it is well known that the resulting Bayes factor involves an arbitrary, unspecified constant, and is thus not well defined. A method of assigning this constant is proposed and illustrated for a number of…

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线性模型的贝叶斯因子与选择准则AI 解读

Summary Global and local Bayes factors are defined and their respective roles examined as choice criteria among alternative linear models. The global Bayes factor is seen to function, in appropriate contexts, as a fully automatic Occam's razor and to be closely related to the Schwarz model choice criterion. The local Bayes factor is shown to have a close relationship with the Akaike Information Criterion.

层次线性模型推断的贝叶斯设计札记AI 解读

Some simple cases of optimal Bayes designs are investigated for linear models with prior information represented in hierarchical form.

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关于“随机变量序列变点推断的贝叶斯方法”的文献提示AI 解读

The author's attention has been drawn to a similar approach: BROEMELING, L. D. (1974). Bayesian inferences about a changing sequence of random variables. Comm. Statist. 3, 243–55.

基于自回归先验的批次验收方案AI 解读

In many batch sampling situations it is reasonable to assume that a correlation exists between the true mean qualities of successively produced batches. A model considered by Campling (1968) is here reanalyzed using the Bayesian linear model framework of Lindley & Smith (1972), and a wider class of serial sampling acceptance schemes derived and compared.

随机变量序列变点推断的贝叶斯方法AI 解读

A Bayesian approach is considered to the problem of making inferences about the point in a sequence of random variables at which the underlying distribution changes. Inferences are based on the posterior probabilities of the possible change-points. Detailed analyses are given for cases in which the distributions are binomial and normal, and numerical illustrations are provided. An informal sequential procedure is also noted.

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.