Uncertainty Analysis for Functional Computer Output: A Simulation Study in Inverse Problems

Computer models with functional output are omnipresent throughout science and engineering. Most often the computer model is treated as a black-box and information about the underlying mathematical model is not exploited in statistical analyses. Consequently, general-purpose bases such as wavelets are typically used to describe the main characteristics of the functional output. In this article we advocate for using information about the underlying mathematical model in order to choose a better basis for the functional output. To validate this choice, a simulation study is presented in the context of uncertainty analysis for a computer model from inverse Sturm-Liouville problems.     

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.     

A Proportional Hazards Regression Model for the Subdistribution with Covariates‐adjusted Censoring Weight for Competing Risks Data

With competing risks data, one often needs to assess the treatment and covariate effects on the cumulative incidence function. Fine and Gray proposed a proportional hazards regression model for the subdistribution of a competing risk with the assumption that the censoring distribution and the covariates are independent. Covariate‐dependent censoring sometimes occurs in medical studies. In this paper, we study the proportional hazards regression model for the subdistribution of a competing risk with proper adjustments for covariate‐dependent censoring. We consider a covariate‐adjusted weight function by fitting the Cox model for the censoring distribution and using the predictive probability for each individual. Our simulation study shows that the covariate‐adjusted weight estimator is basically unbiased when the censoring time depends on the covariates, and the covariate‐adjusted weight approach works well for the variance estimator as well. We illustrate our methods with bone marrow transplant data from the Center for International Blood and Marrow Transplant Research. Here, cancer relapse and death in complete remission are two competing risks.     

Combining Inverse Probability Weighting and Multiple Imputation to Improve Robustness of Estimation

Inverse probability weighting (IPW) and multiple imputation are two widely adopted approaches dealing with missing data. The former models the selection probability, and the latter models data distribution. Consistent estimation requires correct specification of corresponding models. Although the augmented IPW method provides an extra layer of protection on consistency, it is usually not sufficient in practice as the true data‐generating process is unknown. This paper proposes a method combining the two approaches in the same spirit of calibration in sampling survey literature. Multiple models for both the selection probability and data distribution can be simultaneously accounted for, and the resulting estimator is consistent if any model is correctly specified. The proposed method is within the framework of estimating equations and is general enough to cover regression analysis with missing outcomes and/or missing covariates. Results on both theoretical and numerical investigation are provided.     

Parametrizing the Kepler exoplanet period-radius distribution with the bivariate normal inverse Gaussian distribution

This paper presents a simple and robust method for obtaining a comprehensive understanding of the joint period and radius distribution in Kepler exoplanets. The proposed method is based on particle swarm optimization and bivariate Normal Inverse Gaussian distribution. Furthermore, in the construction of the probability density function, this study selects planet-host stars with the GK-type. The injecting approach is also employed to solve the survey completeness of sample. The resulting occurrence rate of Earth analogs is 0.025 with a 95% bootstrap confidence interval between 0.023 and 0.032.     

Cytometry inference through adaptive atomic deconvolution

In this paper, we consider a statistical estimation problem known as atomic deconvolution. Introduced in reliability, this model has a direct application when considering biological data produced by flow cytometers. From a statistical point of view, we aim at inferring the percentage of cells expressing the selected molecule and the probability distribution function associated with its fluorescence emission. We propose here an adaptive estimation procedure based on a previous deconvolution procedure introduced by Es, Gugushvili, and Spreij [(2008), ‘Deconvolution for an atomic distribution’, Electronic Journal of Statistics, 2, 265–297] and Gugushvili, Es, and Spreij [(2011), ‘Deconvolution for an atomic distribution: rates of convergence’, Journal of Nonparametric Statistics, 23, 1003–1029]. For both estimating the mixing parameter and the mixing density automatically, we use the Lepskii method based on the optimal choice of a bandwidth using a bias-variance decomposition. We then derive some convergence rates that are shown to be minimax optimal (up to some log terms) in Sobolev classes. Finally, we apply our algorithm on the simulated and real biological data.     

基于社会需求的高校毕业生就业竞争力研究

社会需求是检验高校毕业生就业竞争力的"试金石"。本文在文献综述的基础上,通过对社会需求单位的调查,构建了高校毕业生就业竞争力评价指标体系;运用层次分析法(AHP)确定了高校毕业生就业竞争力评价指标权重;最后,以某高校为例,采用模糊综合评价方法进行了实证分析,证明了评价指标体系具有一定的实用性和可操作性。     

面向现代航空制造需求的飞行器制造工程专业本科培养方案改革——基于南京航空航天大学实践的思考

现代航空制造技术的发展对本科生的知识结构和培养模式等方面提出了许多新的要求,最主要体现在对专业知识的系统性、课程内容的前沿性、培养模式的实践性等环节的提升。改革的思路沿着现代航空制造技术的发展主线,拓展飞行器制造工程专业的前沿知识框架,建立突出实践环节的模块化专业课程群,提出面向职业规划的套餐式选课,创新综合成绩绩点的评估方法。     

Shrinkage inverse regression estimation for model-free variable selection

Summary.  The family of inverse regression estimators that was recently proposed by Cook and Ni has proven effective in dimension reduction by transforming the high dimensional predictor vector to its low dimensional projections. We propose a general shrinkage estimation strategy for the entire inverse regression estimation family that is capable of simultaneous dimension reduction and variable selection. We demonstrate that the new estimators achieve consistency in variable selection without requiring any traditional model, meanwhile retaining the root n estimation consistency of the dimension reduction basis. We also show the effectiveness of the new estimators through both simulation and real data analysis.