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利用先验信息估计分层总体总量的可容许估计量AI 解读

We consider the problem of the estimation of the total of a stratified finite population. For two levels of prior knowledge about the stratification, we provide Bayes and pseudo-Bayes estimators that make use of this prior knowledge in sensible ways. We then note that admissibility results can be established for these estimators using the techniques of Meeden and Ghosh (1982, 1983) and indicate some possible natural extensions of the present work.

量性响应数据的贝叶斯非参数推断AI 解读

The problem of nonparametric Bayes estimation of a tolerance distribution based on quantal response data has been considered previously with a prior distribution based on the Dirichlet process. In the present article, a broad class of priors is developed for this problem by allowing the hazard function of the tolerance distribution to be a realization of a nonnegative stochastic process with independent increments. This class includes the Dirichlet prior as a special case.…

序贯实验设计的二阶效率AI 解读

In the sequential design of experiments an experimenter performs experiments sequentially to make an eventual inference about the true state of nature. A Bayesian formulation of this problem is considered. The parameter space is assumed finite and there are a finite number of repeatable experiments. Sufficient conditions are given for a procedure to be second order efficient as the sampling costs approach zero. The asymptotic analysis of a related Markov control problem is…

贝叶斯推断中参数模型选择的一则札记AI 解读

This note is concerned with how to replace assessment of a "true" prior on a nonparametric family of distributions--which is usually infeasible--by assessment of an approximating prior with support in a parametrized subfamily, in such a way that the posterior derived from the parametric model is close to the "true" posterior. In general it is not sufficient that the approximating prior be close to the true prior in the sense of weak convergence, and we characterize the…

有限总体模型中贝叶斯最小二乘推断的一则札记AI 解读

This note presents some distribution-free results for incorporating prior information in finite population models. The formulas given are based on modifications of existing Bayesian least squares estimation results and require only the specification of first and second moments of the distributions involved.

利用贝叶斯与经验贝叶斯方法估计参数总体AI 解读

In standard Bayes and empirical Bayes component decision problems, estimating inidividual parameters is the primary goal. In multiple comparison problems and in comparisons of histograms of estimates, however, the primary goal is to produce parameter estimates that can be considered as an ensemble. For example, the histogram of estimates should be a good estimate of the histogram of parameters. Standard methods of estimating by the posterior expectation do minimize…

含趋势与季节性的时间序列平滑先验状态空间建模AI 解读

A smoothness priors modeling of time series with trends and seasonalities is shown. An observed time series is decomposed into local polynomial trend, seasonal, globally stationary autoregressive and observation error components. Each component is characterized by an unknown variance–white noise perturbed difference equation constraint. The constraints or Bayesian smoothness priors are expressed in state space model form. Trading day factors are also incorporated in the…

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Box–Cox 变换线性模型的先验分布选择AI 解读

The noninformative prior distribution for the parameters of the linear model transformed following Box & Cox (1964) has the non-Bayesian property of depending to some extent on the data. An alternative choice of prior which is not outcome-dependent was suggested by Pericchi (1981), but it is argued here that this prior has some undesirable features. An alternative family of non-outcome-dependent priors is suggested, leading to a noninformative prior which is closer in spirit…

交叉分类下的保险损失预测：不同方法的比较AI 解读

Various mathematical and statistical models for estimation of automobile insurance pricing are reviewed. The methods are compared on their predictive ability based on two sets of automobile insurance data for two different states collected over two different periods. The issue of model complexity versus data availability is resolved through a comparison of the accuracy of prediction. The models reviewed range from the use of simple cell means to various…

线性模型的最优贝叶斯实验设计AI 解读

Optimal Bayesian experimental designs for estimation and prediction in linear models are discussed. The designs are optimal for estimating a linear combination of the regression parameters $\mathbf{c}^T\theta$ or prediction at a point where the expected response is $\mathbf{c}^T\mathbf{\theta}$ under squared error loss. A distribution on $\mathbf{c}$ is introduced to represent the interest in particular linear combinations of the parameters. In the usual notation for linear…

一类贝叶斯非参数估计：第一部分，密度估计AI 解读

Given a positive, normalized kernel and a finite measure on an Euclidean space, we construct a random density by convoluting the kernel with the Dirichlet random probability indexed by the finite measure. The posterior distribution of the random density given a sample is classified. The Bayes estimator of the density function is given.

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一种预测导向的模型选择准则AI 解读

SUMMARY A procedure for model selection is presented which chooses the model that gives the best prediction of the future observation. The predictive distributions associated with each model are compared by means of the logarithmic utility function. For two nested normal linear models, the choice criterion is the product of the posterior odds ratio and a factor depending on the design point of the future observation. Taking appropriate mean values, a criterion is obtained…

正态线性模型判别中标准贝叶斯程序的替代方法AI 解读

We consider the standard Bayesian procedure for discrimination, focusing on its tendency to give low posterior probabilities to some correct models, even in conditions of moderate to large sampling sizes. Furthermore, in some situations that could well occur in practice, the standard procedure is even asymptotically inconsistent. We claim that the explanation is that the standard procedure inflates the posterior probability of the model that has the smallest expected…

因子分析的基础AI 解读

A new approach to factor analysis and related latent variable methods is proposed which is based on data reduction using the idea of Bayesian sufficiency. Considerations of symmetry, invariance and independence are used to determine an appropriate family of models. The results are expressed in terms of linear functions of the manifest variables after the manner of principal components analysis. The approach justifies some of the practices based on the normal theory factor…

局部充分性AI 解读

SUMMARY Non-Bayesian inference is considered for a scalar parameter θ based on a p-dimensional statisticXwhich need not constitute a sufficient reduction of the original data. It is shown that there exists a (p−1)-dimensional statistic A that is jointly second-order locally ancillary for θ near θ0 but that, for p > 2, A is not unique even up to nonsingular transformations. To avoid any ambiguity in the resulting inferences, we show that there exists a statistic S, to be…

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Box–Cox 变换线性模型的先验分布选择AI 解读

The noninformative prior distribution for the parameters of the linear model transformed following Box & Cox (1964) has the non-Bayesian property of depending to some extent on the data. An alternative choice of prior which is not outcome-dependent was suggested by Pericchi (1981), but it is argued here that this prior has some undesirable features. An alternative family of non-outcome-dependent priors is suggested, leading to a noninformative prior which is closer in spirit…