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具有相关自相关随机效应的混合模型系统的经验贝叶斯分析AI 解读

Empirical Bayes concepts are implemented in a simultaneous analysis of a system of mixed linear models having linked and serially correlated random effects. Emphasis is placed on the estimation of the random effects and exploration of the relationships between them. Application is made to the investigation of several series of laboratory assay data that were observed during overlapping time intervals and were therefore subjected to common systematic errors, or “daily…

使用 Jeffreys 先验的广义线性模型贝叶斯分析AI 解读

Generalized linear models (GLM's) have proved suitable for modeling various kinds of data consisting of exponential family response variables with covariates. Bayesian analysis of such data requires specification of a prior for the regression parameters in the model used. Uniform priors are very commonly used as conventional noninformative priors. We show, however, that uniform priors for GLM's can lead to improper posterior distributions thus making them undesirable.…

给定先验边际分布时的贝叶斯推断AI 解读

We show how to find bounds on posterior expectations of arbitrary functions of the parameters when the prior marginals are specified but when the complete joint prior is unspecified. We also give a theorem that is useful for finding posterior bounds in a wide range of Bayesian robustness problems. We apply these techniques to two examples. The first example involves a recent clinical trial for extracorporeal membrane oxygenation (ECMO). Our analysis may be regarded as a…

贝叶斯研究者如何预期彼此的信念AI 解读

Our goal is to study general properties of one Bayesian's subjective beliefs about the behavior of another Bayesian's subjective beliefs. We consider two Bayesians, A and B, who have different subjective distributions for a parameter θ, and study Bayesian A's expectation of Bayesian B's posterior distribution for θ given some data Y. We show that when θ can take only two values, Bayesian A always expects Bayesian B's posterior distribution to lie between the prior…

多元总体选择的贝叶斯与极小极大样本可容许程序AI 解读

Let P be a class of independent populations each having an underlying multivariate normal distribution with unknown mean vector. Independent vector samples of common size n are drawn from each population in P. We say that a subset G of P is δ*-Pareto-optimal (in P) if no other population in P has the property that each component of its mean vector is larger by at least δ* ≥ 0 than the corresponding component of the mean vector of any given population in G. This article…

合并无偏与可能有偏估计量的 James–Stein 型方法AI 解读

We present a method for combining unbiased sample data with possibly biased auxiliary information. The estimator we derive is similar in spirit to the James–Stein estimator. We prove that the estimator dominates the sample mean under quadratic loss. When the auxiliary information is unbiased, our estimator has risk slightly greater than the usual combined estimator. As the bias increases, however, the risk of the usual estimator is unbounded, while the risk of our estimator…

单参数情形下最大似然估计与后验均值的比较AI 解读

Consider estimation of a scalar parameter θ of a distribution on the basis of a random sample of size n. Possible estimators include the maximum likelihood estimator, n , and the posterior mean with respect to some prior distribution, n . In this article n and n are compared by considering a large-sample version of the Pitman nearness criterion; conditions are given under which n is preferable to n in this sense. Several examples are provided that show that comparisons of n…

有限总体抽样区间估计的无信息贝叶斯方法AI 解读

A noninformative Bayesian approach to interval estimation in finite population sampling is discussed. Given the sample, this method introduces the Polya distribution as a pseudo posterior distribution over the unobserved members of the population. In many cases this distribution yields interval estimates similar to those of standard frequentist theory. In addition, it can be used in situations where the standard methods are difficult to apply, for example, in producing an…

确定性函数的贝叶斯预测及计算机试验设计AI 解读

This article is concerned with prediction of a function y(t) over a (multidimensional) domain T, given the function values at a set of “sites” {t (1), t (2), …, t (n)} in T, and with the design, that is, with the selection of those sites. The motivating application is the design and analysis of computer experiments, where t determines the input to a computer model of a physical or behavioral system, and y(t) is a response that is part of the output or is calculated from it.…

混沌系统的似然与贝叶斯预测AI 解读

There has recently been considerable interest in both applied disciplines and in mathematics, as well as in the popular science literature, in the areas of nonlinear dynamical systems and chaotic processes. By a nonlinear, deterministic dynamical system, we mean a time series in which, starting at some initial condition, the values of the series are some fixed, nonlinear function of the previous states. One of the more intriguing aspects of these models is their propensity…

摘要暂缺

多元总体选择的贝叶斯与极小极大样本可容许程序AI 解读

Let P be a class of independent populations each having an underlying multivariate normal distribution with unknown mean vector. Independent vector samples of common size n are drawn from each population in P. We say that a subset G of P is δ*-Pareto-optimal (in P) if no other population in P has the property that each component of its mean vector is larger by at least δ* ≥ 0 than the corresponding component of the mean vector of any given population in G. This article…

具有相联系自相关随机效应的混合模型系统的经验贝叶斯分析AI 解读

Empirical Bayes concepts are implemented in a simultaneous analysis of a system of mixed linear models having linked and serially correlated random effects. Emphasis is placed on the estimation of the random effects and exploration of the relationships between them. Application is made to the investigation of several series of laboratory assay data that were observed during overlapping time intervals and were therefore subjected to common systematic errors, or “daily…

有限总体抽样区间估计的无信息贝叶斯方法AI 解读

A noninformative Bayesian approach to interval estimation in finite population sampling is discussed. Given the sample, this method introduces the Polya distribution as a pseudo posterior distribution over the unobserved members of the population. In many cases this distribution yields interval estimates similar to those of standard frequentist theory. In addition, it can be used in situations where the standard methods are difficult to apply, for example, in producing an…

贝叶斯分析者如何预期彼此的信念AI 解读

Our goal is to study general properties of one Bayesian's subjective beliefs about the behavior of another Bayesian's subjective beliefs. We consider two Bayesians, A and B, who have different subjective distributions for a parameter θ, and study Bayesian A's expectation of Bayesian B's posterior distribution for θ given some data Y. We show that when θ can take only two values, Bayesian A always expects Bayesian B's posterior distribution to lie between the prior…

聚焦贝叶斯方法：导言AI 解读

This special section of the Theory and Methods section of the Journal of the American Statistical Association honors Morris H. DeGroot, who died November 2, 1989. It contains his last paper, which was being written at the time of his death. Morrie DeGroot was the founding editor of Statistical Science, which published an issue (Vol. 6, No. 1) in 1991 in his honor. That issue contains an excellent biography of Morrie. Morrie was, of course, a Bayesian. This special section is…

混沌系统的似然与贝叶斯预测AI 解读

There has recently been considerable interest in both applied disciplines and in mathematics, as well as in the popular science literature, in the areas of nonlinear dynamical systems and chaotic processes. By a nonlinear, deterministic dynamical system, we mean a time series in which, starting at some initial condition, the values of the series are some fixed, nonlinear function of the previous states. One of the more intriguing aspects of these models is their propensity…

一类光滑函数的边际尾概率近似及其在贝叶斯与条件推断中的应用AI 解读

This paper presents an asymptotic approximation of marginal tail probabilities for a real-valued function of a random vector, where the function has continuous gradient that does not vanish at the mode of the joint density of the random vector. This approximation has error O(n−3/2) and improves upon a related standard normal approximation which has error O(n−½). Derivation involves the application of a tail probability formula given by DiCiccio, Field & Fraser (1990) to an…

删失数据线性回归模型的精确近似条件推断与贝叶斯推断方法AI 解读

A method to approximate marginal posterior distribution functions of regression coefficients and scale parameters is presented. It is based on a general asymptotic formula of DiCiccio, Field & Fraser (1990) for approximating marginal tail probabilities. In developing the method, it is shown that the accuracy of the approximation of DiCiccio et al. can be substantially increased in certain cases by using a suitable change of variables, and a general approach to deriving such…

理解单位根研究者：鸟瞰式导览AI 解读

For the first-order univariate autoregression without constant term, the joint density (corresponding to a flat prior) for the true coefficient and its least squares estimate is estimated by Monte Carlo and graphically displayed. The graphs show how a symmetric distribution for the coefficient conditional on the estimate coexists with an asymmetric distribution for the estimate conditional on the coefficient. Prior densities implicit in treating classical significance levels…

贝叶斯回归模型中的稳健最高后验密度区域AI 解读

A Bayesian analysis of the linear regression model with only parts of the prior distribution specified or a robust Bayesian analysis lead to sets of posterior distributions. E. E. Leamer (1978) describes the region of posterior means for conjugate priors and varying prior covariance matrices. As an extension to Bayesian confidence sets (HPD regions) the authors introduce the concept of HiFi (high fiduciary) regions. The Hifi region is a union of HPD regions and is a tool for…

贝叶斯路径与单位根：先验问题始终值得争论AI 解读

Abstract This paper provides detailed responses to the following eight discussants of my paper ‘To criticize the critics: an objective Bayesian analysis of stochastic trends’: Gary Koop and Mark Steel; Edward Learner; In‐Moo Kim and G. S. Maddala; Dale J. Poirier; Peter C. Schotman and Herman K. van Dijk; James H. Stock; David DeJong and Charles H. Whiteman; and Christopher Sims. This reply puts new emphasis on the call made in the earlier paper for objective Bayesian…

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