Learning from a lot: Empirical Bayes for high‐dimensional model‐based prediction

Empirical Bayes is a versatile approach to “learn from a lot” in two ways: first, from a large number of variables and, second, from a potentially large amount of prior information, for example, stored in public repositories. We review applications of a variety of empirical Bayes methods to several well‐known model‐based prediction methods, including penalized regression, linear discriminant analysis, and Bayesian models with sparse or dense priors. We discuss “formal” empirical Bayes methods that maximize the marginal likelihood but also more informal approaches based on other data summaries. We contrast empirical Bayes to cross‐validation and full Bayes and discuss hybrid approaches. To study the relation between the quality of an empirical Bayes estimator and p, the number of variables, we consider a simple empirical Bayes estimator in a linear model setting. We argue that empirical Bayes is particularly useful when the prior contains multiple parameters, which model a priori information on variables termed “co‐data”. In particular, we present two novel examples that allow for co‐data: first, a Bayesian spike‐and‐slab setting that facilitates inclusion of multiple co‐data sources and types and, second, a hybrid empirical Bayes–full Bayes ridge regression approach for estimation of the posterior predictive interval.     

Linear scalar-on-surface random effects regression models

Many research fields increasingly involve analyzing data of a complex structure. Models investigating the dependence of a response on a predictor have moved beyond the ordinary scalar-on-vector regression. We propose a regression model for a scalar response and a surface (or a bivariate function) predictor. The predictor has a random component and the regression model falls in the framework of linear random effects models. We estimate the model parameters via maximizing the log-likelihood with the ECME (Expectation/Conditional Maximization Either) algorithm. We use the approach to analyze a data set where the response is the neuroticism score and the predictor is the resting-state brain function image. In the simulations we tried, the approach has better performance than two other approaches, a functional principal component regression approach and a smooth scalar-on-image regression approach.     

China’s Choice of Analytical Models for Its Anti-Monopoly Law

Modern analytical models for anti-monopoly laws are a core element of the application of those laws. Since the Anti-Monopoly Law of the People’s Republic of China was promulgated in 2008, law enforcement and judicial authorities have applied different analytical models, leading to divergent legal and regulatory outcomes as similar cases receive different verdicts. To select a suitable analytical model for China’s Anti-Monopoly Law, we need to consider the possible contribution of both economic analysis and legal formalism and to learn from the mature systems and experience of foreign countries. It is also necessary to take into account such binding constraints as the current composition of China’s anti-monopoly legal system, the ability of implementing agencies and the supply of economic analysis, in order to ensure complementarity between the analytical model chosen and the complexity of economic analysis and between the professionalism of implementing agencies and the cost of compliance for participants in economic activities. In terms of institutional design, the models should provide a considered explanation of the legislative aims of the law’s provisions. It is necessary, therefore, to establish a processing model of behavioral classification that is based on China’s national conditions, applies analytical models using normative comprehensive analysis, makes use of the distribution rule of burden of proof, improves supporting systems related to analytical models and enhances the ability of public authorities to implement the law.     

融合内容分析和关联分析的短生命周期体验品需求特征模式挖掘方法研究

挖掘特定产品的需求模式无法从整体掌握该类产品的市场特征；短生命周期体验品因缺乏历史销售数据，并且销售总量波动性极大，尤其需要从整体掌握销售总量与产品属性间关系的需求特征规律，但又难以挖掘，亟待提出适用于该类产品的需求特征模式挖掘方法。基于按销售总量分区后各区的需求特征的规律性，提出了一种按销售总量分区、以已有产品介绍集和销售总量为源信息、适用于新产品开发前使用、融合内容分析和关联分析的短生命周期体验品需求特征模式挖掘方法。该方法包括基于内容分析法的产品属性挖掘方法和基于关联分析的产品属性关系模式挖掘方法。前者可以得到较全面的产品属性；后者能够构建不同销售总量区间内产品集的属性关系模式，得到各区间的产品属性关系网，获得高销售总量区间具备，但中、低区间不具备的属性关系模式，从而获得需求特征模式。通过不断更新产品介绍集和销售总量并迭代挖掘，该方法能够动态挖掘需求特征模式。最后利用2013至2016年国产犯罪和爱情类电影数据验证了该方法的可行性，并得到了这两类电影的产品属性及近年的需求特征模式，可用于指导这两类电影的创作。     

Assessing the market values of soccer players – a robust analysis of data from German 1. and 2. Bundesliga

The paper examines to what extent a player's market value depends on his skills. Therefore, a data set covering 28 performance measures and the market values of about 493 players from 1. and 2. German Bundesliga is analysed. Applying robust analysis techniques, we are able to robustly estimate market values of soccer players. The results show (1) that there are significantly underrated and overrated players and (2) that a player's affiliation to a certain team may contribute to his market value. We conclude that a club's reputation affects the market values of its players and that star players are in tendency overrated.     

伸展构造背景下倾角资料的构造解释

系统总结了在伸展构造背景下，导致反映构造特征的地层倾角模式复杂化的多种因素。沉积相的不同、岩性变化、井眼状况和测井作业时间等多种因素都可能使地层倾角资料复杂化。进一步指出在拉张盆地中，进行倾角资料的构造解释，必须了解其构造样式的多样性和复杂性，解释存在的多解性。重点解剖了铲式断层在横剖面情况下，对于不同构造位置下的倾角模式。详细分析了一个倾角模式对应多种构造样式的倾角构造解释实例。倾角资料的构造解释应是综合解释，既要综合井筒的相关地质资料，又要综合测井与地质知识，还必须考虑综合地震资料。     

Random effects regression mixtures for analyzing infant habituation

Random effects regression mixture models are a way to classify longitudinal data (or trajectories) having possibly varying lengths. The mixture structure of the traditional random effects regression mixture model arises through the distribution of the random regression coefficients, which is assumed to be a mixture of multivariate normals. An extension of this standard model is presented that accounts for various levels of heterogeneity among the trajectories, depending on their assumed error structure. A standard likelihood ratio test is presented for testing this error structure assumption. Full details of an expectation-conditional maximization algorithm for maximum likelihood estimation are also presented. This model is used to analyze data from an infant habituation experiment, where it is desirable to assess whether infants comprise different populations in terms of their habituation time.     

Conditional time-dependent nonparametric estimators with an application to healthcare production function

ABSTRACT

By using the probabilistic framework of production efficiency, the paper develops time-dependent conditional efficiency estimators performing a non-parametric frontier analysis. Specifically, by applying both full and quantile (robust) time-dependent conditional estimators, it models the dynamic effect of health expenditure on countries’ technological change and technological catch-up levels. The results from the application reveal that the effect of per capita health expenditure on countries’ technological change and technological catch-up is nonlinear and is subject to countries’ specific income levels.     

Risk factors for child maltreatment in South Korea: An investigation of a nationally representative sample

This study investigated the risk factors associated with the occurrence of child physical and psychological abuse in South Korea based on the ecological theory of child maltreatment. A subsample of 3‐ to 18‐year‐old children from “A Study on the Current State of Child Abuse and Neglect,” a nationally representative study on child abuse and neglect, was utilized for secondary data analysis. The sample was divided into two age groups (third graders in elementary school and below and fourth graders and above). We utilized hierarchical logistic regression for each age group separately to analyze the data. The variables at each level of the system (i.e., ontogenic development, microsystem, and exosystem) were entered into the model in sequential order. The results showed the common risk factors for both age groups are the caregiver's experience of abuse in childhood, the child's problem behavior, exposure to domestic violence, community size, and informal social control. The child's age was also significant in both groups but in the opposite direction. Social support was a significant predictor for the younger age group only, while the caregiver's level of education was significant for the older age group only. Implications for future research and practice are discussed based on the study results.