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协方差矩阵的贝叶斯推断AI 解读

A flexible class of prior distributions is proposed, for the covariance matrix of a multivariate normal distribution, yielding much more general hierarchical and empirical Bayes smoothing and inference, when compared with a conjugate analysis involving an inverted Wishart distribution. A likelihood approximation is obtained for the matrix logarithm of the covariance matrix, via Bellman's iterative solution to a Volterra integral equation. Exact and approximate Bayesian,…

贝叶斯网络中的参数更新AI 解读

A Bayes network is a directed acyclic graph in which the links are quantified by fixed conditional probabilities and the nodes represent random variables. The primary use of the network is to provide an efficient method for updating conditional probabilities in the graph. We consider the consequences of using the network as the computational device for updating parameter estimates in the dynamic linear model, a discrete time Bayesian model. We show that using the network…

自变量缺失的回归分析：综述AI 解读

The literature of regression analysis with missing values of the independent variables is reviewed. Six classes of procedures are distinguished: complete case analysis, available case methods, least squares on imputed data, maximum likelihood, Bayesian methods, and multiple imputation. Methods are compared and illustrated when missing data are confined to one independent variable, and extensions to more general patterns are indicated. Attention is paid to the performance of…

有协变量时相关均值的排序与估计：贝叶斯方法AI 解读

Choosing the largest of several means can be a demanding problem, especially in the presence of a covariate. A hierarchical Bayesian approach to ranking and selection, as well as estimation of related means in the presence of a covariate, is considered. For the multiple slopes model we compute, in addition to the posterior means and standard deviations of the parameters, the posterior probabilities that each mean, at a given value of the covariate, is the largest. The vector…

具有二次方差函数的指数族共轭先验AI 解读

Consider a natural exponential family parameterized by θ. It is well known that the standard conjugate prior on θ is characterized by a condition of posterior linearity for the expectation of the model mean parameter μ. Often, however, this family is not parameterized in terms of θ but rather in terms of a more usual parameter, such at the mean μ. The main question we address is: Under what conditions does a standard conjugate prior on μ induce a linear posterior expectation…

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贝叶斯网络中的参数更新AI 解读

A Bayes network is a directed acyclic graph in which the links are quantified by fixed conditional probabilities and the nodes represent random variables. The primary use of the network is to provide an efficient method for updating conditional probabilities in the graph. We consider the consequences of using the network as the computational device for updating parameter estimates in the dynamic linear model, a discrete time Bayesian model. We show that using the network…

线性回归模型中的贝叶斯估计与实验设计AI 解读

Estimation and Design as a Bayesian Decision Problem Choice of a Prior Distribution Conjugate Prior Distributions Bayes Estimation of the Regression Parameter Optimality and Robustness of the Bayes Estimator Bayesian Interpretation of Estimators Using Non-Bayesian Prior Knowledge Bayes Estimation in Case of Prior Ignorance Further Problems The Design Problem for the Linear Bayes Estimator Characterization of Optimal Designs Construction of Optimal Continuous Designs…

具有二次方差函数的指数族共轭先验AI 解读

Consider a natural exponential family parameterized by θ. It is well known that the standard conjugate prior on θ is characterized by a condition of posterior linearity for the expectation of the model mean parameter μ. Often, however, this family is not parameterized in terms of θ but rather in terms of a more usual parameter, such at the mean μ. The main question we address is: Under what conditions does a standard conjugate prior on μ induce a linear posterior expectation…

非线性假设的 Bayes 因子与似然分布AI 解读

New methods are proposed which allow Bayes factors to be computed for hypotheses which impose nonlinear restrictions on the parameters. Projection methods are used to induce the prior distribution over the restricted parameter space which is required for computation of the Bayes factor. Various distance metrics are introduced to define the projection, including a utility-based metric which gives Kullback-Leibler divergence as a special case. Draws from the restricted and…

随机游走与变点备择下的回归系数恒定性检验AI 解读

The locally best invariant statistic to test for the constancy of regression coefficients under a random walk alternative is shown to be the same as a Bayesian-type statistic derived under a change-point alternative. Asymptotic theory for this and more general statistics is discussed.

重返论争前线AI 解读

This study updates previous work by the author providing quantitative evidence of the professional impact of the Bayesian viewpoint as measured by the percentage of pages devoted to Bayesian articles in leading statistics and econometrics journals over the period 1982–1991.

将元分析结果用于贝叶斯更新：空单元格问题AI 解读

Bayesian estimation incorporating prior information has been a popular approach to gaining estimation efficiency. Although prior information can take a variety of forms, generalizations derived from meta-analyses have been suggested as being useful. This article shows that these priors can be problematic in light of the many empty cells observed in meta-analysis designs. Design reduction, which gives rise to an unbiased prior, is found to be the preferred solution.

总量冲击与宏观经济波动：贝叶斯方法AI 解读

Abstract This paper describes Bayesian techniques for analysing the effects of aggregate shocks on macroeconomic time‐series. Rather than calculate point estimates of the response of a time‐series to an aggregate shock, we calculate the whole probability density function of the response and use Monte‐Carlo or Gibbs sampling techniques to evaluate its properties. The proposed techniques impose identification restrictions in a way that includes the uncertainty in these…

似不相关回归模型的预测AI 解读

SUMMARY The seemingly unrelated regressions model is described and analysed from a Bayesian perspective. The predictive density for this model cannot, in general, be evaluated analytically. Two approximations are proposed and investigated. These are Gibbs sampling and a first-order approximation based on a Bayes estimate of the precision matrix. These approximations are then compared on simulated data and both appear to give good results. Extensions to allow for missing data…

跟踪软件可靠性增长的非齐次自回归过程及贝叶斯分析AI 解读

SUMMARY We motivate a non-homogeneous autoregressive process as a model for reliability growth and consider two formulations, both Bayesian, which alleviate a limitation that least squares estimators for such processes of order greater than 1 exist only when repeated measurements of the time series are available. In one formulation, the prior assumption involves exchangeability of coefficients, whereas in the other an autoregressive structure is imposed on them. Both…

近似贝叶斯因子与正交参数：两个二项比例相等性检验AI 解读

SUMMARY We use asymptotic expansions to approximate Bayes factors, improving on a method used by Jeffreys. Suppose that the hypothesis H 0: ψ = ψ0 is to be tested against H A: ψ ≠ ψ0 in the presence of a nuisance parameter β, and initially priors π0(β) under H 0 and π(β, ψ) under H A are used. We consider the problem of assessing sensitivity of the Bayes factor to small changes in π0 and π. We show that for local alternatives (which, for moderate sample sizes, are consistent…

统计双联篇：可容许推断与对称马尔可夫链的常返性AI 解读

Given a parametric model and an improper prior distribution, the formal posterior distribution induces decision rules in any decision problem. The results here provide conditions under which this formal Bayes method produces admissible decision rules for all quadratically regular decision problems. The conditions derived are shown to be equivalent to the recurrence of a natural symmetric Markov chain (on the parameter space) generated by the model and the improper prior. The…

非独立同分布数据下弹着精度分位数的可行贝叶斯估计AI 解读

An important measure of accuracy for problems of directing projectiles at targets is the circular error probable (CEP), a bivariate version of a 50% quantile point. This article presents a Bayesian procedure for estimating CEP when the projectile impact measurements are not iid, which is the case of usual practical interest. Our interest in a Bayesian procedure is motivated by a desire to combine accuracy information from several different sources. Except for the simplest…

利用纵向CD4 T细胞数量研究HIV感染进展的层级贝叶斯模型AI 解读

Taking the absolute number of CD4 T-cells as a marker of disease progression for persons infected with the human immunodeficiency virus (HIV), we model longitudinal series of such counts for a sample of 327 subjects in the San Francisco Men's Health Study (Waves 1–8, excluding zidovudine cases). We conduct a fully Bayesian analysis of these data. We employ individual level nonlinear models incorporating such critical features as incomplete and unbalanced data, population…

贝叶斯与非贝叶斯方法的折中：简要综述AI 解读

Various compromises that have occurred between Bayesian and non-Bayesian methods are reviewed. (A citation is provided that discusses the inevitability of compromises within the Bayesian approach.) One example deals with the masses of elementary particles, but no knowledge of physics will be assumed.

改进 Gibbs 抽样：Gibbs Stopper 与 Griddy-Gibbs 方法AI 解读

The article briefly reviews the history, literature, and form of the Gibbs sampler. An importance sampling device is proposed for converting the output of the Gibbs sampler to a sample from the exact posterior. This Gibbs stopper technique is also useful for assessing convergence of the Gibbs sampler for moderate sized problems. Also presented is an approach for implementing the Gibbs sampler in nonconjugate situations. The basic idea is to approximate the true cdf of each…

利用条件密度混合估计层级模型边际后验密度AI 解读

A technique called quantile integration is proposed for the estimation of marginal posterior densities arising in Bayesian models having hierarchical representations. The method is based on approximating marginal densities as mixtures of conditional densities, where the conditioning variables are selected deterministically from the mixing distributions. The form of the approximation makes it easy to implement, and the resulting approximations are computationally efficient to…

利用条件密度混合估计层级模型边际后验密度的方法AI 解读

A technique called quantile integration is proposed for the estimation of marginal posterior densities arising in Bayesian models having hierarchical representations. The method is based on approximating marginal densities as mixtures of conditional densities, where the conditioning variables are selected deterministically from the mixing distributions. The form of the approximation makes it easy to implement, and the resulting approximations are computationally efficient to…