Bayesian estimation of the generalized lognormal distribution using objective priors

The generalized lognormal distribution plays an important role in analysing data from different life testing experiments. In this paper, we consider Bayesian analysis of this distribution using various objective priors for the model parameters. Specifically, we derive expressions for the Jeffreys-type priors, the reference priors with different group orderings of the parameters, and the first-order matching priors. We also study the properties of the posterior distributions of the parameters under these improper priors. It is shown that only two of them result in proper posterior distributions. Numerical simulation studies are conducted to compare the performances of the Bayesian estimators under the considered priors and the maximum likelihood estimates. Finally, a real-data application is also provided for illustrative purposes.     

Regression Analysis of Longitudinal Data with Time‐Dependent Covariates and Informative Observation Times

Abstract. Longitudinal data frequently occur in many studies, and longitudinal responses may be correlated with observation times. In this paper, we propose a new joint modelling for the analysis of longitudinal data with time‐dependent covariates and possibly informative observation times via two latent variables. For inference about regression parameters, estimating equation approaches are developed and asymptotic properties of the proposed estimators are established. In addition, a lack‐of‐fit test is presented for assessing the adequacy of the model. The proposed method performs well in finite‐sample simulation studies, and an application to a bladder tumour study is provided.     

Bayesian inference for power law processes with applications in repairable systems

Statistical models for recurrent events are of great interest in repairable systems reliability and maintenance. The adopted model under minimal repair maintenance is frequently a nonhomogeneous Poisson process with the power law process (PLP) intensity function. Although inference for the PLP is generally based on maximum likelihood theory, some advantages of the Bayesian approach have been reported in the literature. In this paper it is proposed that the PLP intensity be reparametrized in terms of (β,η), where β is the elasticity of the mean number of events with respect to time and η is the mean number of events for the period in which the system was actually observed. It is shown that β and η are orthogonal and that the likelihood becomes proportional to a product of gamma densities. Therefore, the family of natural conjugate priors is also a product of gammas. The idea is extended to the case that several realizations of the same PLP are observed along overlapping periods of time. Some Monte Carlo simulations are provided to study the frequentist behavior of the Bayesian estimates and to compare them with the maximum likelihood estimates. The results are applied to a real problem concerning the determination of the optimal periodicity of preventive maintenance for a set of power transformers. Prior distributions are elicited for β and η based on their operational interpretation and engineering expertise.     

论高校学生信息档案管理网络化

高校学生信息管理工作是一项极其繁重的工作。随着高校办学规模的不断扩大、学生人数和专业设置的增加,先前的人工管理方式已经不能适应高校发展的需求。针对目前高校学生信息管理复杂而低效的现状,提出学生信息网络化管理系统的构想,对学生信息档案网络化管理进行了探讨。     

略论信息思维的三种基本形式

对于什么是信息思维,当前有一些认识仅从"信息"概念出发作思考,难以触及信息思维的本质,不能很好地指导实践。从信息科学技术的实践中,归纳出信息思维的三种基本形式:确定性思维,即追求信息的保真性、实时性和多维化;控制性思维,即确定信息的系统、反馈机制及容纳干扰;智能化思维,即建立信息模型、模拟现实和去人工化。指出信息思维通过内在的矛盾运动,成为当今指导实践的"思维范式"。     

Mixture reduction via predictive scores

This paper explores the problem of reducing a mixture of conjugate priors to a smaller mixture, from the perspective of the application of a distance measure between priors. The analysis focuses on mixtures of Dirichlet priors, but it has wider applicability. In respect to the proposed scheme, it emerges that for mixtures of -distributions a simple moment-matching reduction procedure is optimal and very good for the more general case of Dirichlet mixtures.     

Sufficient dimension reduction through informative predictor subspace

The purpose of this paper is to define the central informative predictor subspace to contain the central subspace and to develop methods for estimating the former subspace. Potential advantages of the proposed methods are no requirements of linearity, constant variance and coverage conditions in methodological developments. Therefore, the central informative predictor subspace gives us the benefit of restoring the central subspace exhaustively despite failing the conditions. Numerical studies confirm the theories, and real data analyses are presented.     

Accounting for uncertainty in the historical response rate of the standard treatment in single‐arm two‐stage designs based on Bayesian power functions

In phase II single‐arm studies, the response rate of the experimental treatment is typically compared with a fixed target value that should ideally represent the true response rate for the standard of care therapy. Generally, this target value is estimated through previous data, but the inherent variability in the historical response rate is not taken into account. In this paper, we present a Bayesian procedure to construct single‐arm two‐stage designs that allows to incorporate uncertainty in the response rate of the standard treatment. In both stages, the sample size determination criterion is based on the concepts of conditional and predictive Bayesian power functions. Different kinds of prior distributions, which play different roles in the designs, are introduced, and some guidelines for their elicitation are described. Finally, some numerical results about the performance of the designs are provided and a real data example is illustrated. Copyright © 2016 John Wiley & Sons, Ltd.     

Posterior Odds with a Generalized Hyper-g-Prior

Averaged orthogonal rotations of Zellner's g-prior yield general, interpretable, closed form Bayes factors for the normal linear model variable selection problem. Coupled with a model space prior that balances the weight between the identifiable and the unidentifiable models, limiting forms for the posterior odds ratios are seen to yield new expressions for high dimensional model choice.