A Bayesian Model for Markov Chains via Jeffrey's Prior

Abstract

This work deals with the problem of Bayesian estimation of the transition probabilities associated with multistate Markov chain. The model is based on the Jeffreys' noninformative prior. The Bayesian estimator is approximated by means of MCMC techniques. A numerical study by simulation is done in order to compare the Bayesian estimator with the maximum likelihood estimator.     

自然语言理解综述

为了解决计算机理解自然语言问题，产生了自然语言理解这一研究方向，文章归纳了自然语言理解研究中的一些关键问题，整理了国内外自然语言理解技术发展的简史，讨论了自然语言理解技术的主要进展，并针对重大的研究工作做了粗浅的评述。最后对该学科的研究前景进行了展望。     

X波段六角晶系铁氧体吸收剂

讨论了六角晶系铁氧体[(Zn_(1-x)CO_x)_2-W]系列的磁特性及吸波特性。介绍了用特殊工艺制备这种材料的工艺原理及制作过程。用这种吸收剂制备成的吸波涂层具有吸波特性好,工作频带宽等特点。     

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.     

Reference priors for a product of normal means when variances are unknown

The reference priors of Berger and Bernardo (1992) are derived for normal populations with unknown variances when the product of means is of interest. The priors are also shown to be Tibshirani's (1989) matching priors.     

The empirical Bayes estimators of the parameter of the Poisson distribution with a conjugate gamma prior under Stein's loss function

For the hierarchical Poisson and gamma model, we calculate the Bayes posterior estimator of the parameter of the Poisson distribution under Stein's loss function which penalizes gross overestimation and gross underestimation equally and the corresponding Posterior Expected Stein's Loss (PESL). We also obtain the Bayes posterior estimator of the parameter under the squared error loss and the corresponding PESL. Moreover, we obtain the empirical Bayes estimators of the parameter of the Poisson distribution with a conjugate gamma prior by two methods. In numerical simulations, we have illustrated: The two inequalities of the Bayes posterior estimators and the PESLs; the moment estimators and the Maximum Likelihood Estimators (MLEs) are consistent estimators of the hyperparameters; the goodness-of-fit of the model to the simulated data. The numerical results indicate that the MLEs are better than the moment estimators when estimating the hyperparameters. Finally, we exploit the attendance data on 314 high school juniors from two urban high schools to illustrate our theoretical studies.     

A Method to Handle Zero Counts in the Multinomial Model

In the context of an objective Bayesian approach to the multinomial model, Dirichlet(a, …, a) priors with a < 1 have previously been shown to be inadequate in the presence of zero counts, suggesting that the uniform prior (a = 1) is the preferred candidate. In the presence of many zero counts, however, this prior may not be satisfactory either. A model selection approach is proposed, allowing for the possibility of zero parameters corresponding to zero count categories. This approach results in a posterior mixture of Dirichlet distributions and marginal mixtures of beta distributions, which seem to avoid the problems that potentially result from the various proposed Dirichlet priors, in particular in the context of extreme data with zero counts.     

生命信息的交融互渗——中国花鸟画审美初探

自然界的有生命之物,以其不同的形状、色彩、气息和动静之态,而有着不同的审美价值.它们的美是生命之美.中国花鸟画不以再现自然对象的外形为目的,而以思想、情感、意趣等生命现象的高级形式反映在作品中.作者根据主观的审美理想和自我生命的节律加以重新创造,使其固定为物化状态,给人以美的滋养.     

Bayesian Conditional Mean Estimation in Log‐Normal Linear Regression Models with Finite Quadratic Expected Loss

Log‐normal linear regression models are popular in many fields of research. Bayesian estimation of the conditional mean of the dependent variable is problematic as many choices of the prior for the variance (on the log‐scale) lead to posterior distributions with no finite moments. We propose a generalized inverse Gaussian prior for this variance and derive the conditions on the prior parameters that yield posterior distributions of the conditional mean of the dependent variable with finite moments up to a pre‐specified order. The conditions depend on one of the three parameters of the suggested prior; the other two have an influence on inferences for small and medium sample sizes. A second goal of this paper is to discuss how to choose these parameters according to different criteria including the optimization of frequentist properties of posterior means.     

智力资源对物质资源的部分替代与我国集约经济的发展

任何生产活动都需要一定的资源,投入资源之间会形成一定的比例。在很多情况下,投入资源之间的比例是可变的,即资源之间存在着一定程度的替代关系。理想的状况是,是根据各种资源的稀缺程度、效率等因素对其进行合理组合。根据我国经济发展的状况以及资源秉赋,我国应增加智力资源的投入、减少物质资源的消耗,即实现智力资源对物质资源的部分替代,这种替代具有很强的必要性、可能性和现实性。