Bayesian predictive densities based on latent information priors

Construction methods for prior densities are investigated from a predictive viewpoint. Predictive densities for future observables are constructed by using observed data. The simultaneous distribution of future observables and observed data is assumed to belong to a parametric submodel of a multinomial model. Future observables and data are possibly dependent. The discrepancy of a predictive density to the true conditional density of future observables given observed data is evaluated by the Kullback-Leibler divergence. It is proved that limits of Bayesian predictive densities form an essentially complete class. Latent information priors are defined as priors maximizing the conditional mutual information between the parameter and the future observables given the observed data. Minimax predictive densities are constructed as limits of Bayesian predictive densities based on prior sequences converging to the latent information priors.     

Data-dependent probability matching priors of the second order

In this paper, we consider the preliminary test approach for the estimation of the regression parameter in a multiple regression model under a multicollinearity situation. The preliminary test two-parameter estimators based on the Wald (W), likelihood ratio, and Lagrangian multiplier tests are given, when it is suspected that the regression parameter may be restricted to a subspace and the regression error is distributed with multivariate Student's t distribution. The bias and mean square error of the proposed estimators are derived and compared. The conditions of superiority of the proposed estimators are obtained. Finally, we conclude that the optimum choice of the level of significance becomes the traditional choice by using the Wald test.     

Use of prior information for estimating the variance components

The MINQUE and its modifications are considered for estimating the variances of the balanced one-way random effects model. The effects of the a priori values on the estimators of the variances are examined in detail. The Mean Square Errors of the estimators are compared for variations in the prior values of the unknown variances.     

试论孔子"为政先礼"的治国方略

孔子生活时代 ,“礼”的政治含义和思想内涵是“礼制”、“礼仪”、“礼治”、“礼俗”。孔子建立“礼”治社会的主张和措施是“礼以教人”、当权者率先“好礼”、“克己复礼”。孔子对“礼制”的创新和改革表现为“损益”西周以来的礼制 ,扩大“礼治”的社会基础 ,向传统的“礼教”提出挑战     

Superiority comparisons between mixed regression estimators

This paper gives necessary and sufficient conditions for a mixed regression estimator to be superior to another mixed estimator. The comparisons are based on the mean square error matrices of the estimators. Both estimators are allowed to be biased.     

互联网信息作为现有技术的界定

由于互联网信息的不稳定性和多样性,对于如何在现有法律框架下将互联网信息纳入现有技术的范围存有诸多困难,在分析互联网信息作为现有技术特征的基础上,该文认为,应从以下三个方面将互联网信息界定为现有技术：在公开的时间上,主要应通过建立“豁免网站”名单来确定;在公开方式和地域上,完全可以将互联网信息作为其他的公开方式;在公众可获取性上,应在对互联网信息内容分类的基础上进行区别考虑。同时,对于其他特殊情况则应进行个案分析。     

On Bayesian estimators in multistage binomial designs

A new class of Bayesian estimators for a proportion in multistage binomial designs is considered. Priors belong to the beta-J distribution family, which is derived from the Fisher information associated with the design. The transposition of the beta parameters of the Haldane and the uniform priors in fixed binomial experiments into the beta-J distribution yields bias-corrected versions of these priors in multistage designs. We show that the estimator of the posterior mean based on the corrected Haldane prior and the estimator of the posterior mode based on the corrected uniform prior have good frequentist properties. An easy-to-use approximation of the estimator of the posterior mode is provided. The new Bayesian estimators are compared to Whitehead's and the uniformly minimum variance estimators through several multistage designs. Last, the bias of the estimator of the posterior mode is derived for a particular case.     

Bayesian estimation for the Pareto income distribution

The Bayes estimators of the Gini index, the mean income and the proportion of the population living below a prescribed income level are obtained in this paper on the basis of censored income data from a pareto income distribution. The said estimators are obtained under the assumptions of a two-parameter exponential prior distribution and the usual squared error loss function. This work is also extended to the case when the income data are grouped and the exact incomes for the individuals in the population are not available. The method for the assessment of the hyperparameters is also outlined. Finally, the results are generalized for the doubly truncated gamma prior distribution. Now deceased.     

Empirical Bayes estimation of parameters in Markov transition probability matrix with computational methods

Empirical Bayes estimator for the transition probability matrix is worked out in the cases where we have belief regarding the parameters, For example, where the states seem to be equal or not. In both cases, priors are in accordance with our beliefs. Using EM algorithm, computational methods for different hyperparameters of the empirical Bayes are described. Also, robustness of empirical Bayes procedure is investigated.     

论先刑后民原则

我国司法实践中对于刑民交叉案件,在处理机制上主要依据先刑后民原则,该原则是否应被看作一种法律原则来适用,其是否有法律依据,如何界定该原则的适用范围,以及对其存在的意义如何评价,是主要阐述的问题.