On the mathematics of the Jeffreys–Lindley paradox

This paper is concerned with the well known Jeffreys–Lindley paradox. In a Bayesian set up, the so-called paradox arises when a point null hypothesis is tested and an objective prior is sought for the alternative hypothesis. In particular, the posterior for the null hypothesis tends to one when the uncertainty, i.e., the variance, for the parameter value goes to infinity. We argue that the appropriate way to deal with the paradox is to use simple mathematics, and that any philosophical argument is to be regarded as irrelevant.     

A note on the mean residual life of a coherent system with a cold standby component

In this paper, we investigate the effect of a cold standby component on the mean residual life (MRL) of a system. When the system fails, a cold standby component is immediately put in operation. We particularly focus on the coherent systems in which, after putting the standby component into operation, the failure of the system is due to the next component failure. For these systems, we define MRL functions and obtain their explicit expressions. Also some stochastic ordering results are provided. Such systems include k-out-of-n systems. Hence, our results extend some results in literature.     

Feature screening in ultrahigh-dimensional additive Cox model

The additive Cox model is flexible and powerful for modelling the dynamic changes of regression coefficients in the survival analysis. This paper is concerned with feature screening for the additive Cox model with ultrahigh-dimensional covariates. The proposed screening procedure can effectively identify active predictors. That is, with probability tending to one, the selected variable set includes the actual active predictors. In order to carry out the proposed procedure, we propose an effective algorithm and establish the ascent property of the proposed algorithm. We further prove that the proposed procedure possesses the sure screening property. Furthermore, we examine the finite sample performance of the proposed procedure via Monte Carlo simulations, and illustrate the proposed procedure by a real data example.     

Effect of tuberculosis on immune restoration among HIV-infected patients receiving antiretroviral therapy

In this article, time to immune recovery during antiretroviral therapy was estimated and compared between HIV-infected children with and without tuberculosis (TB). CD4?T-cell restoration was used as a criterion for determining immune recovery. The median residual lifetime function, which is more intuitive and robust compared to the frequently used measures of lifetime data, was used to estimate time to CD4?T-cell restoration. The median residual lifetime is not influenced by extreme observations and heavy-tailed distributions which are commonly encountered in clinical studies. Permutation-based methods were used to compare the CD4?T-cell restoration times between the two groups of patients. Our results indicate that children with TB had uniformly higher median residual lifetimes to immune recovery compared to those without TB. Although TB was associated with slower CD4?T-cell restoration, the differences between the restoration times of the two groups were not statistically significant.     

A robust automatic clustering algorithm for probability density functions with application to categorizing color images

This study develops a robust automatic algorithm for clustering probability density functions based on the previous research. Unlike other existing methods that often pre-determine the number of clusters, this method can self-organize data groups based on the original data structure. The proposed clustering method is also robust in regards to noise. Three examples of synthetic data and a real-world COREL dataset are utilized to illustrate the accurateness and effectiveness of the proposed approach.     

Conditional covariance penalties for mixed models

The prediction error for mixed models can have a conditional or a marginal perspective depending on the research focus. We introduce a novel conditional version of the optimism theorem for mixed models linking the conditional prediction error to covariance penalties for mixed models. Different possibilities for estimating these conditional covariance penalties are introduced. These are bootstrap methods, cross-validation, and a direct approach called Steinian. The behavior of the different estimation techniques is assessed in a simulation study for the binomial-, the t-, and the gamma distribution and for different kinds of prediction error. Furthermore, the impact of the estimation techniques on the prediction error is discussed based on an application to undernutrition in Zambia.     

An algorithmic approach to construct D-optimal saturated designs for logistic model

In this paper, locally D-optimal saturated designs for a logistic model with one and two continuous input variables have been constructed by modifying the famous Fedorov exchange algorithm. A saturated design not only ensures the minimum number of runs in the design but also simplifies the row exchange computation. The basic idea is to exchange a design point with a point from the design space. The algorithm performs the best row exchange between design points and points form a candidate set representing the design space. Naturally, the resultant designs depend on the candidate set. For gain in precision, intuitively a candidate set with a larger number of points and the low discrepancy is desirable, but it increases the computational cost. Apart from the modification in row exchange computation, we propose implementing the algorithm in two stages. Initially, construct a design with a candidate set of affordable size and then later generate a new candidate set around the points of design searched in the former stage. In order to validate the optimality of constructed designs, we have used the general equivalence theorem. Algorithms for the construction of optimal designs have been implemented by developing suitable codes in R.     

工程质量政府监督多层次利益分配与激励协同机制探究

The implementation of the government supervision of the quality of the project is an international practice. The basic form of government supervision of engineering quality is government supervision on the quality behavior of the engineering main bodies and its results by the competent government department entrusted. Its essence is a dual principal-agent process. The frequent accidents of the engineering quality reflect the loss and failure of the government law enforcement supervision of the engineering quality to some extent. Its root lies in the lack of endogenous power in the law enforcement supervision of the project quality government supervisors in the law enforcement supervision. Therefore, the incentive coordination mechanism of the government supervision based on the multi-level interest distribution is worth explored. In views of the multi-level management system which is formed by the government departments, government quality supervision organizations, quality supervision team (or group) for the government supervision of engineering quality. The benefit distribution function between every party is constructed, and the game model of the multi-level incentive and coordination for the government supervision in engineering quality is built. To solve and deduce from the first stage of the cooperative game and the second stage of the non-cooperative game, the cooperative game can obtain the reward coefficient: . The coordination degree of the best effort can be obtained by the non cooperative game. The result shows that:the coordination degree of government engineering quality supervisor is related to the coordination costs, and had nothing to do with fixed costs. The benefit distribution coefficient not only depends on the efforts of the quality government monitors, but also on the efficiency of other parties' efforts. The quality supervisors of the project will also focus on the coordination with other parties when enhancing their management capabilities to improve the overall performance of project quality government supervision. The strategy of the incentive coordination mechanism for the supervision and cooperation of the project quality government is:the government quality supervision team should set up the supervisory team properly, improve the coordination efficiency and reduce the cost of supervision-coordination to maximize the value of self-motivation. Quality supervision team (or group) should establish the partnership to improve the coordination efficiency for achieving the maximization of their own incentive value.The model and conclusion of incentive synergy mechanism based on multi-level benefit allocation mechanism are researched. It can provide theoretical support and practice reference for the market governance and supervision of general public goods.     

Sexual Beliefs and Sexual Functioning: The Mediating Role of Cognitive Distraction

Dysfunctional sexual beliefs are vulnerability factors for sexual dysfunction. This cross-sectional study aimed to test the mediating role of cognitive distraction on the relationship between dysfunctional sexual beliefs about sexual functioning shared by men and women and sexual function. The authors used a sample of 421 cisgender heterosexual participants involved in a monogamous relationship. The hypothesized mediation model was tested using a bootstrapped cross product of coefficients approach. Results showed a significant negative, indirect effect between dysfunctional sexual beliefs and women's sexual function through cognitive distraction. The discussion of this study highlights the importance of cognitive factors in sexual functioning.