Complex Latent Variable Modeling in Educational Assessment

Bayesian item response theory models have been widely used in different research fields. They support measuring constructs and modeling relationships between constructs, while accounting for complex test situations (e.g., complex sampling designs, missing data, heterogenous population). Advantages of this flexible modeling framework together with powerful simulation-based estimation techniques are discussed. Furthermore, it is shown how the Bayes factor can be used to test relevant hypotheses in assessment using the College Basic Academic Subjects Examination (CBASE) data.     

Computing maximum likelihood estimates from type II doubly censored exponential data

It is well-known that, under Type II double censoring, the maximum likelihood (ML) estimators of the location and scale parameters, θ and δ, of a twoparameter exponential distribution are linear functions of the order statistics. In contrast, when θ is known, theML estimator of δ does not admit a closed form expression. It is shown, however, that theML estimator of the scale parameter exists and is unique. Moreover, it has good large-sample properties. In addition, sharp lower and upper bounds for this estimator are provided, which can serve as starting points for iterative interpolation methods such as regula falsi. Explicit expressions for the expected Fisher information and Cramér-Rao lower bound are also derived. In the Bayesian context, assuming an inverted gamma prior on δ, the uniqueness, boundedness and asymptotics of the highest posterior density estimator of δ can be deduced in a similar way. Finally, an illustrative example is included.     

一种混合的垃圾邮件过滤算法研究

贝叶斯邮件过滤器具有较强的分类能力,极高的准确率,在内容过滤领域占据主导地位。人工免疫系统具备强大的自学习、自适应,鲁棒性等能力,已发展成为计算智能研究的一个崭新的分支。该文在分析贝叶斯的原理和人工免疫的仿生机理的基础上,将贝叶斯与人工免疫相结合,设计和实现了一种基于贝叶斯和人工免疫的混合垃圾邮件过滤算法,并利用现有的垃圾邮件语料库得到预期的实验结果。     

基于改进PCA的朴素贝叶斯分类算法

朴素贝叶斯是一种处理分类问题的常用方法,但它的属性条件独立性假设在实际应用中难以成立,导致其分类性能降低。针对这一问题,文章提出了基于改进PCA的朴素贝叶斯分类算法,该算法通过Pearson和Kendall系数计算出属性间的相关性大小,基于主成分分析筛选出新的属性集,使其尽量满足条件独立性假设,并对新数据集进行朴素贝叶斯分类。实验结果表明,该方法有效地提高了分类准确率。     

Bayes and Empirical Bayes Inference in Changepoint Problems

ABSTRACT

In the case of the random design nonparametric regression, the double smoothing technique is applied to estimate the multivariate regression function. The proposed estimator has desirable properties in both the finite sample and the asymptotic cases. In the finite sample case, it has bounded conditional (and unconditional) bias and variance. On the other hand, in the asymptotic case, it has the same mean square error as the local linear estimator in Fan (Design-Adaptive Nonparametric Regression. Journal of the American Statistical Association 1992, 87, 998–1004; Local Linear Regression Smoothers and Their Minimax Efficiencies. Annals of Statistics 1993, 21, 196–216). Simulation studies demonstrate that the proposed estimator is better than the local linear estimator, because it has a smaller sample mean integrated square error and gives smoother estimates.     

Parameter estimation for switched counting processes

The paper investigates parameter estimation problems in special Markov modulated counting processes. The events occuring at any state of an underlying Markov chain can be equipped with marks performing additional information on the events. Specifying the model to the case of two-state Markov chain modulation, the so-called switched counting process, some statistical problems are studied:maximum likelihood estimators, Rao-Blackwell optimal estimators, test of equality of the counting intensities of the two states and minimax estimation procedures. Tne consideration could be applied in various practical problems, in particular, in queueing and in reliability models, for example in failure-repair processes with alternatively operating repair systems.     

A Comparison of Bayes Factors for Separated Models: Some Simulation Results

Some alternative Bayes Factors: Intrinsic, Posterior, and Fractional have been proposed to overcome the difficulties presented when prior information is weak and improper prior are used. Additional difficulties also appear when the models are separated or non nested. This article presents both simulation results and some illustrative examples analysis comparing these alternative Bayes factors to discriminate among the Lognormal, the Weibull, the Gamma, and the Exponential distributions. Simulation results are obtained for different sample sizes generated from the distributions. Results from simulations indicates that these alternative Bayes factors are useful for comparing non nested models. The simulations also show some similar behavior and that when both models are true they choose the simplest model. Some illustrative example are also presented.     

基于Bayes需求预测更新的供应链合作策略研究

在预测误差与提前期成对数线性关系,赶工成本与提前期成分段线性关系条件下,研究了基于Bayes需求预测更新的易逝品供应链合作策略问题.通过建立零售商独立决策的优化模型,讨论了模型最优解的存在性,论证了供应链合作的必要性.进一步提出了三参数的供应链风险分担契约来协调分散决策的供应链,分析了实现供应链渠道协调的条件.并通过数值分析和参数的灵敏度分析说明了上述结论以及算法.分析结果表明,这种供应链契约不仅能够实现供应链利润最大化,而且能够通过契约参数的调整,按照供应链成员增值能力的大小灵活划分供应链成员之间的利润分配比例.     

ESTIMATION OF THE PARAMETER OF A POISSON DISTRIBUTION USING A LINEX LOSS FUNCTION

This paper considers estimation of the parameter of a Poisson distribution using Varian's (1975) asymmetric LINEX loss function L (δ) = b{exp(aδ) - aδ - 1}, where δ is the estimation error and b > 0, a 0. It is shown that for a < 0, the sample mean X¯ is admissible whereas for a > 0, X¯ is dominated by c*X¯, where c*= (n/a)log(1+a/n). Practical implications of this result are indicated. More general results, concerning the admissibility of estimators of the form cX¯+ d are also presented.     

Bayesian point null hypothesis testing via the posterior likelihood ratio

This paper gives an exposition of the use of the posterior likelihood ratio for testing point null hypotheses in a fully Bayesian framework. Connections between the frequentist P-value and the posterior distribution of the likelihood ratio are used to interpret and calibrate P-values in a Bayesian context, and examples are given to show the use of simple posterior simulation methods to provide Bayesian tests of common hypotheses.