Variance components estimation for the balanced random effects model under mixed prior distributions

For the balanced random effects models, when the variance components are correlated either naturally or through common prior structures, by assuming a mixed prior distribution for the variance components, we propose some new Bayesian estimators. To contrast and compare the new estimators with the minimum variance unbiased (MVUE) and restricted maximum likelihood estimators (RMLE), some simulation studies are also carried out. It turns out that the proposed estimators have smaller mean squared errors than the MVUE and RMLE.     

Comparison of testing procedures utilizing P-values and Bayes factors in some common situations

Bayesian alternatives to classical tests for several testing problems are considered. One-sided and two-sided sets of hypotheses are tested concerning an exponential parameter, a Binomial proportion, and a normal mean. Hierarchical Bayes and noninformative Bayes procedures are compared with the appropriate classical procedure, either the uniformly most powerful test or the likelihood ratio test, in the different situations. The hierarchical prior employed is the conjugate prior at the first stage with the mean being the test parameter and a noninformative prior at the second stage for the hyper parameter(s) of the first stage prior. Fair comparisons are attempted in which fair means the likelihood of making a type I error is approximately the same for the different testing procedures; once this condition is satisfied, the power of the different tests are compared, the larger the power, the better the test. This comparison is difficult in the two-sided case due to the unsurprising discrepancy between Bayesian and classical measures of evidence that have been discussed for years. The hierarchical Bayes tests appear to compete well with the typical classical test in the one-sided cases.     

On the choice of the prior distribution in hypergeometric sampling

Information in a statistical procedure arising from sources other than sampling is called prior information, and its incorporation into the procedure forms the basis of the Bayesian approach to statistics. Under hypergeometric sampling, methodology is developed which quantifies the amount of information provided by the sample data relative to that provided by the prior distribution and allows for a ranking of prior distributions with respect to conservativeness, where conservatism refers to restraint of extraneous information embedded in any prior distribution. The most conservative prior distribution from a specified class (each member of which carries the available prior information) is that prior distribution within the class over which the likelihood function has the greatest average domination. Four different families of prior distributions are developed by considering a Bayesian approach to the formation of lots. The most conservative prior distribution from each of the four families of prior distributions is determined and compared for the situation when no prior information is available. The results of the comparison advocate the use of the Polya (beta-binomial) prior distribution in hypergeometric sampling.     

Approximate minimax estimation in linear regression: theoretical results

We consider to ordinary linear regression model where the parameter vector ß is constrained to a given ellipsoid. It will be shown that within the class of linear statistics for ß where exists a (sub-)sequence of approximate minimax estimators converging to an exact minimax estimator. This result is valid for an arbitrary quadratic loss function.     

Isotonic rules for selecting good exponential populations

The problem of selecting exponential populations better than a control under a simple ordering prior is investigated. Based on some prior information, it is appropriate to set lower bounds for the concerned parameters. The information about the lower bounds of the concerned parameters is taken into account to derive isotonic selection rules for the control known case. An isotonic selection rule for the control unknown case is also proposed. A criterion is proposed to evaluate the performance of the selection rules. Simulation comparisons among the performances of several selection rules are carried out. The simulation results indicate that for the control known case, the new proposed selection rules perform better than some earlier existing selection rules.     

Spatial Pattern and Determinants of Age at Marriage in Nigeria Using a Geo-Additive Survival Model

Age at first marriage, after controlling for socio-economic and demographic variables, varies across regions and districts. A geo-additive hazard model allows for measuring spatial effects. The nonlinear and baseline effects are modeled by Bayesian penalized splines; spatial components are treated as correlated random effects following a Markov random field. Application is based on data from 1999, 2003, and 2008 Nigeria Demographic and Health Surveys. Age at first marriage is positively associated with education and urbanization and depends on religion. It presents a north-south divide.     

基于贝叶斯神经网络短期负荷预测模型

本文提出了基于贝叶斯神经网络(BNN)短期负荷预测模型。根据气象影响因素和电力负荷的样本数据,针对权向量参数的先验分布分别为正态分布和柯西分布两种情况,应用混合蒙特卡洛(HMC)算法学习了BNN的权向量参数。由HMC算法和Laplace算法学习的贝叶斯神经网络以及BP算法学习的传统神经网络分别对4月 (春)、8月 (夏)、10月 (秋)和1月(冬)每月25天的每个整点时刻的负荷进行了预测。这些神经网络的输入层有11个节点,它们分别与每个整点时刻和的气象因素、上一个整点时刻的气象因素和时间变量相对应,输出层只有一个节点,它与负荷变量对应。试验结果表明HMC算法学习的BNN的预测结果的百分比平均绝对误差( MAPE)和平方根平均误差( RSME )取值远远小于由Laplace 算法学习的BNN和BP算法学习的人工神经网络的 MAPE和RMSE。 而且,HMC算法学习的BNN在测试集和训练集上的预测误差MAPE和RMSE的相差很小。 实验结果充分说明HMC算法学习的BNN具有较高的预测精度和较强的泛化能力。     

我国独立董事制度的反思与重构

独立董事制度与现代经济学的信息不对称理论、委托代理理论、信号传递理论和资源依赖理论密不可分。独立董事的引入,优化了我国上市公司董事会的构成,有效减轻了内部人控制带来的众多问题。然而,我国独立董事制度尚需要进一步完善。文章从独立董事的定位、独立董事"独立性"的判断标准、独立董事的特别职责等方面提出了重构我国独立董事制度的思路和建议。     

Adaptive smoothing in associated kernel discrete functions estimation using Bayesian approach

This paper demonstrates that cross-validation (CV) and Bayesian adaptive bandwidth selection can be applied in the estimation of associated kernel discrete functions. This idea is originally proposed by Brewer [A Bayesian model for local smoothing in kernel density estimation, Stat. Comput. 10 (2000), pp. 299–309] to derive variable bandwidths in adaptive kernel density estimation. Our approach considers the adaptive binomial kernel estimator and treats the variable bandwidths as parameters with beta prior distribution. The best variable bandwidth selector is estimated by the posterior mean in the Bayesian sense under squared error loss. Monte Carlo simulations are conducted to examine the performance of the proposed Bayesian adaptive approach in comparison with the performance of the Asymptotic mean integrated squared error estimator and CV technique for selecting a global (fixed) bandwidth proposed in Kokonendji and Senga Kiessé [Discrete associated kernels method and extensions, Stat. Methodol. 8 (2011), pp. 497–516]. The Bayesian adaptive bandwidth estimator performs better than the global bandwidth, in particular for small and moderate sample sizes.     

Bayesian analysis in multivariate regression models with conjugate priors

In this paper, we consider the full rank multivariate regression model with matrix elliptically contoured distributed errors. We formulate a conjugate prior distribution for matrix elliptical models and derive the posterior distributions of mean and scale matrices. In the sequel, some characteristics of regression matrix parameters are also proposed.