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方差分量模型的贝叶斯方法AI 解读

An exact Bayesian analysis can be performed for normal theory variance components models, using importance sampling. But remarkably accurate approximations are available using the Laplacian T-approximation introduced by Leonard, Hsu, and Ritter. Instead of maximizing the joint posterior density, conditional upon the parameter of interest, a device described by O'Hagan is used first. The Bayesian estimators are compared to the Lindley—Stein shrinkage estimators and the…

方差分量模型的贝叶斯方法AI 解读

An exact Bayesian analysis can be performed for normal theory variance components models, using importance sampling. But remarkably accurate approximations are available using the Laplacian T-approximation introduced by Leonard, Hsu, and Ritter. Instead of maximizing the joint posterior density, conditional upon the parameter of interest, a device described by O'Hagan is used first. The Bayesian estimators are compared to the Lindley—Stein shrinkage estimators and the…

矩阵对数协方差模型AI 解读

A flexible method is introduced to model the structure of a covariance matrix C and study the dependence of the covariances on explanatory variables by observing that for any real symmetric matrix A, the matrix exponential transformation, C = exp (A), is a positive definite matrix. Because there is no constraint on the possible values of the upper triangular elements on A, any possible structure of interest can be imposed on them. The method presented here is not intended to…

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,…

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…

贝叶斯边际推断AI 解读

A method is proposed for approximating the marginal posterior density of a continuous function of several unknown parameters, thus permitting inferences about any parameter of interest for nonlinear models when the sample size is finite. Possibly tedious numerical integrations are replaced by conditional maximizations, which are shown to be quite accurate in a number of special cases. There are similarities with the profile likelihood ideas originated by Kalbfleisch and…

贝叶斯边际推断AI 解读

A method is proposed for approximating the marginal posterior density of a continuous function of several unknown parameters, thus permitting inferences about any parameter of interest for nonlinear models when the sample size is finite. Possibly tedious numerical integrations are replaced by conditional maximizations, which are shown to be quite accurate in a number of special cases. There are similarities with the profile likelihood ideas originated by Kalbfleisch and…

密度估计、随机过程与先验信息AI 解读

Summary A method is proposed for the non-parametric estimation of a probability density, based upon a finite number of observations and prior information about the smoothness of the density. A logistic density transform and a reproducing inner product from the first-order autoregressive stochastic process are employed to represent prior information that the derivative of the transform is unlikely to change radically within small intervals. The posterior estimate of the…

摘要暂缺

多项概率估计与预检验问题的贝叶斯方法AI 解读

New Bayesian estimates are proposed for multinomial probabilities, when the prior distribution is a mixture of Dirichlet distributions. They are based upon a distributional approximation for the χ2 statistic and may be contrasted with the frequentist approximations recommended by other authors. An alternative is also suggested to the χ2 goodness-of-fit test, when it is employed as a preliminary test of significance. The new procedure possesses remarkably different…

作为估计捷径的F检验程序研究AI 解读

Summary When estimating fixed effects in the one-way anova model the F-test for the equality of the group means is sometimes used as a preliminary test of significance. This paper provides alternatives to the percentage points in the F-test by re-formulating the problem under estimation, as opposed to hypothesis testing, criteria. The new procedure possesses strikingly different properties, and it is argued that fixed-size tests are not obviously relevant within an…

参数约束不确定性下的贝叶斯估计AI 解读

When estimating a normal location parameter, an inequality constraint is sometimes indicated by theoretical considerations. If, however, this constraint is assumed a priori definitely to hold, then the data will never be permitted to formally contradict the theory. We propose a family of skew prior distributions which reflect uncertainty about the constraint.

多参数估计的若干替代方法AI 解读

Bayesian and classical alternatives are considered, interpreted, and compared with simultaneous estimation methods in the literature. The main topics explored are the estimation of several normal means, and of several binomial or Poisson parameters. An empirical comparison and three real examples are included.

多参数估计的若干替代方法AI 解读

Bayesian and classical alternatives are considered, interpreted, and compared with simultaneous estimation methods in the literature. The main topics explored are the estimation of several normal means, and of several binomial or Poisson parameters. An empirical comparison and three real examples are included.

参数约束存在不确定性时的贝叶斯估计AI 解读

When estimating a normal location parameter, an inequality constraint is sometimes indicated by theoretical considerations. If, however, this constraint is assumed a priori definitely to hold, then the data will never be permitted to formally contradict the theory. We propose a family of skew prior distributions which reflect uncertainty about the constraint.

二维列联表的贝叶斯估计方法AI 解读

Summary Estimation methods are proposed for the row, column and interaction effects in two-way contingency tables, the one-way table being treated as a special case. The methods are appropriate when the parameters are thought a priori to be related to each other. The posterior estimates have the practical effects of smoothing the contingency table, and are valid even if some of the cell frequencies are zero. The main case treated is where particular assumptions of…